Maxwell built upon Faraday's discoveries concerning lines of force of both electric charges and magnetic poles through the application of mathematics.
Every wave has a particular apeed:
Water: v = sqrt(qy/2pi)
Sound: v = sqrt(p/dr)
Linked oscillators: v = sqrt(k/m)
Maxwell attempted to determine the speed of waves in Faraday's lines of force. These forces were similar to the following equations:
F(g) = -G m1m2/r^2 (r^)
F(e) = ke q1q2/r^2 (r^)
F(m) = km p1p2/r^2 (r^)
Specific constants:
G = 6.7 x 10^-11 Nm^2/kg^2
ke = 9 x 10^9 Nm^2/ c^2
km = 1 x 10^-7 Ns^2/c^2
Since these equations are not independent, ke and km are related:
ke/km = 3 x 10^8 m/s^2 or the speed of light where both magnetic and electric waves propogate at the speed of light.
The medium through which these waves propagate is the electromagnetic field, and they obey these equations:
0integral(integral( B dA)) = 0
E(o)d/dtintegral(integral( E dA)) = I
0integral( B dr) = u(o) (I + E(o)d/dt integral(integral(E dA)))
0integral( E dr) = 0
With every electric wave, there is also a magnetic wave.
Friday, April 6, 2012
Lesson 38 Alternating Current
Alternating current (AC) is an oscillating current. It is created by a voltage that rises and falls.
Direct current (DC) is a steady flow of electricity where, idealy, its voltage is constant and equal to the current, that is also constant, multiplied by effective resistance of the circuit.
Consider a circuit that consists of an alternating voltage source, a capacitor, and an inductor. According to the mathematical rules of Gustav Kircchoff, the rises in voltage at the source is never greater than E(o) which is equivalent to the sum of voltage drops around the circuit.
E(o)sinwt = LdI/dt + q/c
The result is a differential equation that can be written in terms of charge q on the capacitor.
= Ld^2/dt^2 + q/c
E(o)sinwt = m(Ld^2/dt^2) + kx this same equation describes the displacement x of a harmonic oscillator.
Both equations lead to resonance, which, in a circuit can cause the flow of a great amount of charge.
Radio and television signals are transfered through electric resonance.
A capacitor opposes change in positive or negative charge, while an inductor opposes change in current in the same manner the intertial mass on a spring opposes change in velocity.
In an AC, if the frequency is low enough the charging and discharging of the capacitor can keep up with the oscillating applied voltage. At higher frequency, the capacitor cannot charge and discharge fast enough. Therefore, no voltage difference develops across it and nearly all voltage is across the resistor.
If an inductor is in the circuit at low frequency there is time for voltage to build within it and not across. In high frequency the voltage cannot change fast enough so most of the voltage is across the inductor.
When all elements are in the same circuit at low frequency, most voltage charges and discharges the capacitor. At higher frequency, most of the voltage is used changing the current in the inductor. If the frequency is at the resonant frequency, quite a large current flows.
Power = current x voltage
P = IV
Heating = P^2R/V^2
Therefore, the higher the voltage the less power is lst in transit over long distances along electric wires.
If AC passes through a loop of coil, a constantly changing magnetic flux is produced. If a set of coils of wires are wrapped around an iron loop, the flux is completely contained. This flux produces voltage.
Voltage can be increased or decreased safely with this method due to the fact that voltage is proportional to the number of coils of wire around the iron loop.
This is the reason AC won over DC in the modern world.
Direct current (DC) is a steady flow of electricity where, idealy, its voltage is constant and equal to the current, that is also constant, multiplied by effective resistance of the circuit.
Consider a circuit that consists of an alternating voltage source, a capacitor, and an inductor. According to the mathematical rules of Gustav Kircchoff, the rises in voltage at the source is never greater than E(o) which is equivalent to the sum of voltage drops around the circuit.
E(o)sinwt = LdI/dt + q/c
The result is a differential equation that can be written in terms of charge q on the capacitor.
= Ld^2/dt^2 + q/c
E(o)sinwt = m(Ld^2/dt^2) + kx this same equation describes the displacement x of a harmonic oscillator.
Both equations lead to resonance, which, in a circuit can cause the flow of a great amount of charge.
Radio and television signals are transfered through electric resonance.
A capacitor opposes change in positive or negative charge, while an inductor opposes change in current in the same manner the intertial mass on a spring opposes change in velocity.
In an AC, if the frequency is low enough the charging and discharging of the capacitor can keep up with the oscillating applied voltage. At higher frequency, the capacitor cannot charge and discharge fast enough. Therefore, no voltage difference develops across it and nearly all voltage is across the resistor.
If an inductor is in the circuit at low frequency there is time for voltage to build within it and not across. In high frequency the voltage cannot change fast enough so most of the voltage is across the inductor.
When all elements are in the same circuit at low frequency, most voltage charges and discharges the capacitor. At higher frequency, most of the voltage is used changing the current in the inductor. If the frequency is at the resonant frequency, quite a large current flows.
Power = current x voltage
P = IV
Heating = P^2R/V^2
Therefore, the higher the voltage the less power is lst in transit over long distances along electric wires.
If AC passes through a loop of coil, a constantly changing magnetic flux is produced. If a set of coils of wires are wrapped around an iron loop, the flux is completely contained. This flux produces voltage.
Voltage can be increased or decreased safely with this method due to the fact that voltage is proportional to the number of coils of wire around the iron loop.
This is the reason AC won over DC in the modern world.
Lesson 37 Electromagnetic Induction
Electromagnetic induction is the basis for all electrical advancement and electrical discoveries.
Michael Faraday developed the world's first electric motor, where a charged wire follows the circular magnetic field created by the electric current.
Electromagnetic induction is how a magnetic field drives an electric current around a circuit.
Magnetic fields apply forces to electric charges, but only if the charges are in motion.
F=qV x B
The direction of the force is perpendicular to the velocity and the field, and depends on the sign of the charge (negative in this case). Moving a wire charged with electrons through a magnetic field causes the current to flow.
The field of a bar magnet can be perpendicular to every point of a circular loop of wire. Moving the loop drives a current around the loop. Moving the loop up drives the current one way, and moving the loop down drives the current another way. This also applies if the magnet is moved.
Any method of changing magnetic field makes current flow. This causes a change in magnetic flux which changes the current flow as if by voltage. E = d (IO) or Faraday's law. of electro magnetic induction.
Continually rotating a loop of wire in a magnetic field changes the current in the loop. The resulting voltage and current are sinusoidal, going first one way and then the other.
Current flows through a coil of wire when the magnetic flux through it is changing, the current flows one way if the flux decreases and the other way when the flux increases. The current induced in the wire creates a flux of its own, whose direction depends on the dircetion of the current. The flux created by the induced current always opposes a change in the external flux. This is known as Lenz'z law.
An electric current in any circuit creates a magnetic field which whenever it changes induces a current in the same circuit that opposes changes. This is called self-induction.
The induction of a circuit element:
E = -L dI/dt L= (dIO)/dI
Both resstors and capacitor exhibit self-induction. Electric fields will only circulate if magnetic flux is changed.
E = Ointegral(E dr) = -d/dt integral(integral(B dA))
Michael Faraday developed the world's first electric motor, where a charged wire follows the circular magnetic field created by the electric current.
Electromagnetic induction is how a magnetic field drives an electric current around a circuit.
Magnetic fields apply forces to electric charges, but only if the charges are in motion.
F=qV x B
The direction of the force is perpendicular to the velocity and the field, and depends on the sign of the charge (negative in this case). Moving a wire charged with electrons through a magnetic field causes the current to flow.
The field of a bar magnet can be perpendicular to every point of a circular loop of wire. Moving the loop drives a current around the loop. Moving the loop up drives the current one way, and moving the loop down drives the current another way. This also applies if the magnet is moved.
Any method of changing magnetic field makes current flow. This causes a change in magnetic flux which changes the current flow as if by voltage. E = d (IO) or Faraday's law. of electro magnetic induction.
Continually rotating a loop of wire in a magnetic field changes the current in the loop. The resulting voltage and current are sinusoidal, going first one way and then the other.
Current flows through a coil of wire when the magnetic flux through it is changing, the current flows one way if the flux decreases and the other way when the flux increases. The current induced in the wire creates a flux of its own, whose direction depends on the dircetion of the current. The flux created by the induced current always opposes a change in the external flux. This is known as Lenz'z law.
An electric current in any circuit creates a magnetic field which whenever it changes induces a current in the same circuit that opposes changes. This is called self-induction.
The induction of a circuit element:
E = -L dI/dt L= (dIO)/dI
Both resstors and capacitor exhibit self-induction. Electric fields will only circulate if magnetic flux is changed.
E = Ointegral(E dr) = -d/dt integral(integral(B dA))
Sunday, April 1, 2012
Lesson 36 Vector Fields and Hydrodynamics
A disturbance in a field propagates at the speed of light. The study of hydrodynamics led to theories regarding fields of force. The fields of electricity, magnetism, and water are all similar in nature.
The flow of water can be modeled by vectors. Electric forces on a test charge can be represened by a pattern of vectors in space. So can the magnetized needle and its direction in space.
0integral(integral( B dA)) = 0
0integral(integral( E dA)) = a/E(o)
0integral( B dr) = u(o) I
0integral( E dr) = 0
All vector fields obey equations describing their forms. The electric flux through any closed surface is proportional to the net electric charge inside. Magnetic flux through any closed surface is equal to zero. The line integral of any electric field of a closed path is zero. The line integral of the magnetic field around a closed path is proportional to the electric current passing through the path.
In terms of hydrodynamics, flux is the total amount of water passing through an element of are with a given amount of time. In time t that's the total amount of water in a box of width vt where
volume = vtA
Therefore the flux of flow rate is volume/t = vA
If the area element is tilted with respect to the flow, less of the water passes through it. Flux depends on the angle between the flow field and the area element. This idea is similar where both magnetic and electric flux are measured by the total number of lines of force passing through a surface in a given area.
Therefore the mathematical expression of flux is the same for all vector fields.
In water, the flux out of a closed surface is zero where
0integral(integral(V dA)) = 0
Electric flux is like the flux of sunlight. The flux of light as it radiates outward is proportional to the strength of the source within the closed surface.
If there is no flux in magnetic and water fields, how do they have flow?
Water:
If water is stirred motion starts from the outside and moves inward. If water circulates, it does so in a vortex flow that is stable. mRV = L or mass times distance from the center times the speed is conserved for each bit of water.
As each bit of water flows closer to the center hole, speed increases as a vortex is formed because angular momentum is conserved.
V = L/m (1/R) 0^
In magnetism, the vectors represent the strength of the field and not speed.
0integral(V dr) = K
The line integral of the velocity field of water is called circulation. Since the water flows in circles with velocity inversely proportional to distance from the core (the circulation around the vortex core) doesn't depend on distance from the core, it is a constant.
In the same way the line integral of a magnetic field is proportional to the electric current that creates the field. The vortex is the source of fluid flow in the same sense that electric current is the source of the magnetic field. Just as electric current makes a closed loop, so can a vortex core form a loop called a vortex ring. The flow field of a vortex ring is the same as the magnetic field of a current loop. And vortex rings like all vortices are stable structures.
Electric, magnetic, or water, each can be expressed through the line integral and flux.
Magnetic fields circulate but never converge to a point, electric fields radiate from point charges but never circulate. Vector fields also have energy. Energy resides in the motion of the fluid, it is kinetic in nature where
Energy/Volume = 1/2(density) v^2
The energy at a point is proportional to the square of the field E, or B.
The flow of water can be modeled by vectors. Electric forces on a test charge can be represened by a pattern of vectors in space. So can the magnetized needle and its direction in space.
0integral(integral( B dA)) = 0
0integral(integral( E dA)) = a/E(o)
0integral( B dr) = u(o) I
0integral( E dr) = 0
All vector fields obey equations describing their forms. The electric flux through any closed surface is proportional to the net electric charge inside. Magnetic flux through any closed surface is equal to zero. The line integral of any electric field of a closed path is zero. The line integral of the magnetic field around a closed path is proportional to the electric current passing through the path.
In terms of hydrodynamics, flux is the total amount of water passing through an element of are with a given amount of time. In time t that's the total amount of water in a box of width vt where
volume = vtA
Therefore the flux of flow rate is volume/t = vA
If the area element is tilted with respect to the flow, less of the water passes through it. Flux depends on the angle between the flow field and the area element. This idea is similar where both magnetic and electric flux are measured by the total number of lines of force passing through a surface in a given area.
Therefore the mathematical expression of flux is the same for all vector fields.
In water, the flux out of a closed surface is zero where
0integral(integral(V dA)) = 0
Electric flux is like the flux of sunlight. The flux of light as it radiates outward is proportional to the strength of the source within the closed surface.
If there is no flux in magnetic and water fields, how do they have flow?
Water:
If water is stirred motion starts from the outside and moves inward. If water circulates, it does so in a vortex flow that is stable. mRV = L or mass times distance from the center times the speed is conserved for each bit of water.
As each bit of water flows closer to the center hole, speed increases as a vortex is formed because angular momentum is conserved.
V = L/m (1/R) 0^
In magnetism, the vectors represent the strength of the field and not speed.
0integral(V dr) = K
The line integral of the velocity field of water is called circulation. Since the water flows in circles with velocity inversely proportional to distance from the core (the circulation around the vortex core) doesn't depend on distance from the core, it is a constant.
In the same way the line integral of a magnetic field is proportional to the electric current that creates the field. The vortex is the source of fluid flow in the same sense that electric current is the source of the magnetic field. Just as electric current makes a closed loop, so can a vortex core form a loop called a vortex ring. The flow field of a vortex ring is the same as the magnetic field of a current loop. And vortex rings like all vortices are stable structures.
Electric, magnetic, or water, each can be expressed through the line integral and flux.
Magnetic fields circulate but never converge to a point, electric fields radiate from point charges but never circulate. Vector fields also have energy. Energy resides in the motion of the fluid, it is kinetic in nature where
Energy/Volume = 1/2(density) v^2
The energy at a point is proportional to the square of the field E, or B.
Lesson 35 The Magnetic Field
Electric currents produce magnetic forces that cause magnets to point perpendicular to the flow of the current. The electric current that flows through a wire creates a magnetic field that circulates around the wire. The strength of the field depends on the distance from the wire where
delta (B) is proportional to K(m) i/r^2 delta (S) r^
a segment of electric current produces a magnetic field proportional to the inverse square of the distance. The direction of the field depends on the direction of the current according to the vector cross product. The field would be largest where the current segment and distance vector are perpendicular. Electric currents cannot exist in tiny segments so B = K(m) I integral (dsr^/r^2).
B = K(m) 2I/R s^ x R^, the field due to current flowing in a long straight wire is always perpendicular to the wire and decreases as the inverse first power of the distance from the wire. The field is in circles concentric to the wire. If the circular field is placed in a loop, a dipole field forms. A solenoid is a stack of current loops and creates a field much like that of a bar magnet. If the solenoid is bent into a circle, it is called a toroid, in which the magnetic field is contained.
Electric charges apply forces of magnetism between each other. The force of electric current is measured by the force between two wires, or amp.
Magnetism is electricity in motion. Ampere theorized that every magnet must have circulating electric current to produce a magnetic field (Electrodynamics).
In an electric field no work is done is a charge is moved in a closed path, therefore the electric potential is constant and the force of the electric field is zero.
The current of a wire creates circles of constant magnetic field. Since the field is constant on each circle, the line integral on each one is easily calculated where
0integral (B dr) = m 2I/R 2piR 0integral or a constant multiplied by the current in the wire.
0integral (B dr) = u(o) I which is the same for any circle around the wire.
This is Ampere's Law:
0integral(integral( B dA)) = 0
0integral(integral( E dA)) = a/E(o)
0integral( B dr) = u(o) I
0integral( E dr) = 0
The law of electricity and magnetism.
delta (B) is proportional to K(m) i/r^2 delta (S) r^
a segment of electric current produces a magnetic field proportional to the inverse square of the distance. The direction of the field depends on the direction of the current according to the vector cross product. The field would be largest where the current segment and distance vector are perpendicular. Electric currents cannot exist in tiny segments so B = K(m) I integral (dsr^/r^2).
B = K(m) 2I/R s^ x R^, the field due to current flowing in a long straight wire is always perpendicular to the wire and decreases as the inverse first power of the distance from the wire. The field is in circles concentric to the wire. If the circular field is placed in a loop, a dipole field forms. A solenoid is a stack of current loops and creates a field much like that of a bar magnet. If the solenoid is bent into a circle, it is called a toroid, in which the magnetic field is contained.
Electric charges apply forces of magnetism between each other. The force of electric current is measured by the force between two wires, or amp.
Magnetism is electricity in motion. Ampere theorized that every magnet must have circulating electric current to produce a magnetic field (Electrodynamics).
In an electric field no work is done is a charge is moved in a closed path, therefore the electric potential is constant and the force of the electric field is zero.
The current of a wire creates circles of constant magnetic field. Since the field is constant on each circle, the line integral on each one is easily calculated where
0integral (B dr) = m 2I/R 2piR 0integral or a constant multiplied by the current in the wire.
0integral (B dr) = u(o) I which is the same for any circle around the wire.
This is Ampere's Law:
0integral(integral( B dA)) = 0
0integral(integral( E dA)) = a/E(o)
0integral( B dr) = u(o) I
0integral( E dr) = 0
The law of electricity and magnetism.
Lesson 34 Magnetism
William Gilbert discovered that one can destroy the magnetic properties of a metal by heating it up. One can increase magnetic power by stroking one metal with another. The earth behaves like a giant magnet. If you keep an iron bar strictly aligned for a long period of time, it will become magnetized.
Stars and planets have magnetic fields.
The equation for the force between two magnetic poles is
F(m) = K(m) (p1p2/r^2) r^
where opposite poles attract and like poles repel.
Unlike electric charges, magnetic poles always come in equal and opposite pairs. Cutting a magnet in half creates two new poles with a north and a south pole.
In the vast universe, some magnetic mono-poles do exist as a result of the Big Bang.
A magnetic field of a magnet with two poles is similar to the electric field of electric charges with equal and opposite charges.
The circular loop of electric current creates a magnetic field of this form. So do all protons, neutrons and electrons. The earth itself has a dipole field that points South, which is why compass needles point North.
In any magnetic field a magnet is subject to equal and opposite forces at its poles, so it tends to line up with the field. The field exerts a torque that makes the north pole point in the direction of the field.
The Earth's magnetic field is impacted by solar winds, thus not extending indefinitely in the solar direction. Earth's tail, much like a comet's, is comprised of magnetic flux.
Magnetic flux is defined in perfect analogy to electric flux, or the flow of the field through any surface.
d I(O) (E) = E dA
Electric flux through a small element of surface is equal to the area multiplied by the component of the electric field perpendicular to it.
The total flux is the sum of all the flux through the surface.
I(O) (E) = integral(integral(E dA))
= 4piK(E)q
or q/epsilon (o)
The flux through any closed surface is equal to a constant times the change inside.
For an electric dipole, Gauss's law applies by balancing outward flux from the positive charge against inward flux from the negative charge. The total flux, like the charge, is zero. Magnetic flux is defined in exactly the same way.
d I(O) (M) = B dA
I(O) (M) = integral(integral(B dA))
= 0
Flux is a measure of the total number of lines of forces passing through any surface.
Since all magnets are dipoles, the total magnetic flux through any closed surface is zero. The outward flux of the north pole and the inward flux of the south pole balance one another.
Any amount of flux put into a magnet releases the same amount of flux (earth). The earth's magnetic field is produced by electric currents due to molten nickel and iron interaction deep beneath the earth's surface.
The magnetic field is continually changing . The earth changes polarity every 500,000 years, where the north and south pole switch roles.
A magnetic field does not apply any force to an electric charge at rest. However, if the electric charge is in motion, the magnetic field applies a force known as the lorentz force where F = qV x B if it is perpendicular both the field and direction of motion of the charge. Since the magnetic force is perpendicular to the velocity, the force does not cause the charge to speed up or slow down. Charges toend to curve around the field in circular or helical paths.
In non-uniform magnetic fields, electric charges can be trapped in the Van Allen radiation belts. Near the polar regions, charged particles get close enough to strike the atmosphere giving off light like the Aurora Borealis at the North and South Pole.
The magnetic field protects the earth from solar flares and winds. Without the magnetic field, life would not be possible on earth.
Stars and planets have magnetic fields.
The equation for the force between two magnetic poles is
F(m) = K(m) (p1p2/r^2) r^
where opposite poles attract and like poles repel.
Unlike electric charges, magnetic poles always come in equal and opposite pairs. Cutting a magnet in half creates two new poles with a north and a south pole.
In the vast universe, some magnetic mono-poles do exist as a result of the Big Bang.
A magnetic field of a magnet with two poles is similar to the electric field of electric charges with equal and opposite charges.
The circular loop of electric current creates a magnetic field of this form. So do all protons, neutrons and electrons. The earth itself has a dipole field that points South, which is why compass needles point North.
In any magnetic field a magnet is subject to equal and opposite forces at its poles, so it tends to line up with the field. The field exerts a torque that makes the north pole point in the direction of the field.
The Earth's magnetic field is impacted by solar winds, thus not extending indefinitely in the solar direction. Earth's tail, much like a comet's, is comprised of magnetic flux.
Magnetic flux is defined in perfect analogy to electric flux, or the flow of the field through any surface.
d I(O) (E) = E dA
Electric flux through a small element of surface is equal to the area multiplied by the component of the electric field perpendicular to it.
The total flux is the sum of all the flux through the surface.
I(O) (E) = integral(integral(E dA))
= 4piK(E)q
or q/epsilon (o)
The flux through any closed surface is equal to a constant times the change inside.
For an electric dipole, Gauss's law applies by balancing outward flux from the positive charge against inward flux from the negative charge. The total flux, like the charge, is zero. Magnetic flux is defined in exactly the same way.
d I(O) (M) = B dA
I(O) (M) = integral(integral(B dA))
= 0
Flux is a measure of the total number of lines of forces passing through any surface.
Since all magnets are dipoles, the total magnetic flux through any closed surface is zero. The outward flux of the north pole and the inward flux of the south pole balance one another.
Any amount of flux put into a magnet releases the same amount of flux (earth). The earth's magnetic field is produced by electric currents due to molten nickel and iron interaction deep beneath the earth's surface.
The magnetic field is continually changing . The earth changes polarity every 500,000 years, where the north and south pole switch roles.
A magnetic field does not apply any force to an electric charge at rest. However, if the electric charge is in motion, the magnetic field applies a force known as the lorentz force where F = qV x B if it is perpendicular both the field and direction of motion of the charge. Since the magnetic force is perpendicular to the velocity, the force does not cause the charge to speed up or slow down. Charges toend to curve around the field in circular or helical paths.
In non-uniform magnetic fields, electric charges can be trapped in the Van Allen radiation belts. Near the polar regions, charged particles get close enough to strike the atmosphere giving off light like the Aurora Borealis at the North and South Pole.
The magnetic field protects the earth from solar flares and winds. Without the magnetic field, life would not be possible on earth.
Lesson 33 Electric Circuits
Controlling the flow of water has allowed civilizations to develop over the course of history. Similarly, electricity is a fluid whose flow can be controlled.
Inventors such as Thomas Edison developed ways to manipulate electricity to illuminate homes and also to produce and distribute electricity through wires and circuits.
The amount of light is determined by the amount of current measured in amps where 1 amp = 1 coulomb/second
Electric current I is the rate of flow of electric charge q, at any instant, the current is the same anywhere along the wire of the circuit. Electric charge is neither created nor destroyed along the way.
I = d/dt
Hans Christian Ørsted used a voltaic pile to deflect a magnetic needle with an electric current and discovered electromagnetism.
Through the use of a voltaic pile, Edison perfected the telegraph, a device where electric current causes a magnet to move in another location, thus enabling long distance communication.
In a telegraph, to prevent signal loss, if the voltage is increased in proportion to the distance.
Ohm's Law - to make a current flow through a conductor a voltage is needed. The current is always proportional to the voltage.
A constant of proportionality is called R or resistance.
V = IR is Ohm's Law
An element with resistance within a current is called a resistor.
Ohm's law does not hold true in all situations, however it is pratical in most.
The amount of electric current that flows through a resistor depends on the voltage drop across it, how wide, how long it is, and what it is made of.
The resistance of an electric resistor is proportional to its length, inversely proportional to its area and proportional to its resistivity to hinder the flow of electrons. This tendency to resist is something all materials have, but to varying degrees. Multiple resistors in a series are called resistor series and is analogous to lengthening the resistor.
Putting resistors side by side increases the area through which electrons can flow (known as resistors in parallel) and have a lower resistance than either one alone.
What resists the flow of electricity in a conductor? In a metal, electrons move constantly in different directions. The electrons orbit with the metal as if it were a molecule. This flow has no resistance and does not create a net flow in or out. If the conductor is in electrostatic equilibrium there is not electric field inside and no voltage difference. If a battery makes electric current flow, equilibrium is destroyed causing an electric field to form within the metal. Inside a perfect crystalline metal, the mobile electrons would continually accelerate. Impurities of crystals cause resistance by preventing acceleration of electrons.
As current flows through a resistor the energy that is turned into heat is equal to the amount of charge of flow multiplied by the change in potential. The rate of heating of power consumed is equal to IV. Using Ohm's law, power can be written as P = IV = I^2R or V^2/R
1 watt = 1 amp x a volt
Conservation of charge and of energy are derived from Ohm's law.
A capacitor in a circuit stores charge.
Time is equal to capacitance, or resistance for capacitor to empty.
Inventors such as Thomas Edison developed ways to manipulate electricity to illuminate homes and also to produce and distribute electricity through wires and circuits.
The amount of light is determined by the amount of current measured in amps where 1 amp = 1 coulomb/second
Electric current I is the rate of flow of electric charge q, at any instant, the current is the same anywhere along the wire of the circuit. Electric charge is neither created nor destroyed along the way.
I = d/dt
Hans Christian Ørsted used a voltaic pile to deflect a magnetic needle with an electric current and discovered electromagnetism.
Through the use of a voltaic pile, Edison perfected the telegraph, a device where electric current causes a magnet to move in another location, thus enabling long distance communication.
In a telegraph, to prevent signal loss, if the voltage is increased in proportion to the distance.
Ohm's Law - to make a current flow through a conductor a voltage is needed. The current is always proportional to the voltage.
A constant of proportionality is called R or resistance.
V = IR is Ohm's Law
An element with resistance within a current is called a resistor.
Ohm's law does not hold true in all situations, however it is pratical in most.
The amount of electric current that flows through a resistor depends on the voltage drop across it, how wide, how long it is, and what it is made of.
The resistance of an electric resistor is proportional to its length, inversely proportional to its area and proportional to its resistivity to hinder the flow of electrons. This tendency to resist is something all materials have, but to varying degrees. Multiple resistors in a series are called resistor series and is analogous to lengthening the resistor.
Putting resistors side by side increases the area through which electrons can flow (known as resistors in parallel) and have a lower resistance than either one alone.
What resists the flow of electricity in a conductor? In a metal, electrons move constantly in different directions. The electrons orbit with the metal as if it were a molecule. This flow has no resistance and does not create a net flow in or out. If the conductor is in electrostatic equilibrium there is not electric field inside and no voltage difference. If a battery makes electric current flow, equilibrium is destroyed causing an electric field to form within the metal. Inside a perfect crystalline metal, the mobile electrons would continually accelerate. Impurities of crystals cause resistance by preventing acceleration of electrons.
As current flows through a resistor the energy that is turned into heat is equal to the amount of charge of flow multiplied by the change in potential. The rate of heating of power consumed is equal to IV. Using Ohm's law, power can be written as P = IV = I^2R or V^2/R
1 watt = 1 amp x a volt
Conservation of charge and of energy are derived from Ohm's law.
A capacitor in a circuit stores charge.
Time is equal to capacitance, or resistance for capacitor to empty.
Lesson 32 The Electric Battery
To understand a battery, understand the process of making a metal. Begin with a positive ion, because it has a positive charge, it creates the potential energy of attraction for the missing electron. Place positive ions adjacent to one another. Add just enough electrons to make a neutral system and arrange in the form of a lattice to create a piece of metal. A positive test charge would detect no change in potential energy and therefore no force anywhere inside or outside the metal. A real electron inside the metal is acted on by all the ions and electrons except for itself, lending itself a net potential energy. If the electron is moved from one part of the metal to another, other electrons flow to replace it so it has the same potential energy everywhere. There is virtually no force preventing an electron from moving freely through the metal. Beyond the surface of the metal, there are no more ions or electrons to balance forces. So to push an electron outside of metal requires a powerful force, creating a real electric potential and leaving a net positive charge on the metal. The overall potential energy of a real electron drops sharply at the metals surface to a lower value that is the same everywhere inside.
The electrons of a metal also have kinetic energy, but not enough to escape. The amount of energy an electron would need to escape from a metal is known as the work function.
Volta developed the perpetual resevoir of electricity, or the electrophorous.
Galvani studied "animal electricity" using frog legs to which he discovered that nerve impulses which excite muscles into action are really electrical sigals which travel everywhere throughout the body.
Why is an electric impulse created when one metal touches another?
Each metal has a work function that keeps electrons from escaping. The work function of copper and zinc differ from one another by the electric potential IV. When two metals are brought into contact the barrier at the interface vanishes. The electrons are free to flow into the metal where they have lowered total energy. As electrons flow, the metal they leave becomes positively charged and the one they enter becomes negatively charged. This creates an electrostatic potential difference that balance the energy difference. The flow stops. If the metals are separated, each has a net electric charge and an electrostatic potential difference between them.
Volta did not have the luxury of the electron, so he developed the voltaic pile.
Suppose two different metals electrically charged from contact are placed in an electrolite, the metal has extra electrons, attracts positive ions from the solution whenever positive ions touch the surface they can extract excess electrons from the metal. Meanwhle, the other metal which lacks electrons attracts negative ions when negative ions reach the surface, the missing electrons can be replaced. So the electrolite drives the metals back to an electrically neutral position. If they were to make direct contact, a new surge of electrons would flow because of their difference in work fucnctions. Now, because of the electrolite, the surge does not cease. Electrons continue to flow from one metal to the other and they are continually replaced by the ions in the solution. Until there is no more chemical energy. This is known as the battery.
The electrons of a metal also have kinetic energy, but not enough to escape. The amount of energy an electron would need to escape from a metal is known as the work function.
Volta developed the perpetual resevoir of electricity, or the electrophorous.
Galvani studied "animal electricity" using frog legs to which he discovered that nerve impulses which excite muscles into action are really electrical sigals which travel everywhere throughout the body.
Why is an electric impulse created when one metal touches another?
Each metal has a work function that keeps electrons from escaping. The work function of copper and zinc differ from one another by the electric potential IV. When two metals are brought into contact the barrier at the interface vanishes. The electrons are free to flow into the metal where they have lowered total energy. As electrons flow, the metal they leave becomes positively charged and the one they enter becomes negatively charged. This creates an electrostatic potential difference that balance the energy difference. The flow stops. If the metals are separated, each has a net electric charge and an electrostatic potential difference between them.
Volta did not have the luxury of the electron, so he developed the voltaic pile.
Suppose two different metals electrically charged from contact are placed in an electrolite, the metal has extra electrons, attracts positive ions from the solution whenever positive ions touch the surface they can extract excess electrons from the metal. Meanwhle, the other metal which lacks electrons attracts negative ions when negative ions reach the surface, the missing electrons can be replaced. So the electrolite drives the metals back to an electrically neutral position. If they were to make direct contact, a new surge of electrons would flow because of their difference in work fucnctions. Now, because of the electrolite, the surge does not cease. Electrons continue to flow from one metal to the other and they are continually replaced by the ions in the solution. Until there is no more chemical energy. This is known as the battery.
Lesson 31 Voltage Energy and Force
Voltage (electric potential) is a measure of the electric charge. The following observation unveils the dilemma between electric force and potential. Electrons in a body are held together by only 3-5v, and batteries cannot shoot electric beams like the Van de Graaff generator.
The electric field is the negative derivative of potential.
v = -integral (E dr)
E = K(e) (q/r^2) r^
V = -K(e) integral (q/r^2 dr)
V = K(e) q/r
The integral of the electric field of a point charge is proportional to 1/r.
It requires no work to move a charge along a curve of constant potential.
The electric field is perpendicular to each equal potential at every point. Electric potential is the ability to do work by making electric charges flow, this potential is measured in volts.
The electric chair was one of the first uses of high voltage (neon lights)
Atoms, the basis of all matter is held together by electricity.
In every atom, the electric force binds negatively charged electrons to a positive nucleus. The nucleus can be considered a point charge even though it is comprised of protons and neutrons. One electron has exactly the amount of negative charge to balance with the positive charge, and result in a perfectly neutral atom.
The distance between the nucleus and the outermost electron is 1 Angstrom = 10^-8 cm.
All other electrons balance with all protons except one, and the remaining electron detects the electric field of the proton only 1 A(o) away.
The electric potential = 14.4 V
U = qV
because charge is negative, so is potential energy at 14.4eV, this must be overcome to remove an electron from an atom:
If an atom and a 100,000 V vandegraph fight over an electron the atom will win. This is not
because of voltage, but force. The derivative of potential energy.
The force of the atom is 100,000 times stronger than that of the Van de Graaff.
In lightning, the molecules of air are momentarily ionized leaving a gas of positive molecular ions and negative electrons called a plasma. The electric force between ions and electrons causes them to recombine into neutral matter giving off excess energy in the form of light.
In a neon light, the process is slowed to a continuous glow, but the electric field in a neon light cannot ionize matter.
The neon light and Van de Graaff generator ionize air through collisions that contains not electric force, but a few accidental electrons that hit other molecules. If the electric field is great enough, thus increasing acceleration and the distance between atoms is large enough, the electron can build enough energy to knock another electron off an atom. This causes a chain reaction due to higher acceleration and a spark.
The force of electricity depends on both voltage and charge. Voltage, energy, and force hold the universe together.
The electric field is the negative derivative of potential.
v = -integral (E dr)
E = K(e) (q/r^2) r^
V = -K(e) integral (q/r^2 dr)
V = K(e) q/r
The integral of the electric field of a point charge is proportional to 1/r.
It requires no work to move a charge along a curve of constant potential.
The electric field is perpendicular to each equal potential at every point. Electric potential is the ability to do work by making electric charges flow, this potential is measured in volts.
The electric chair was one of the first uses of high voltage (neon lights)
Atoms, the basis of all matter is held together by electricity.
In every atom, the electric force binds negatively charged electrons to a positive nucleus. The nucleus can be considered a point charge even though it is comprised of protons and neutrons. One electron has exactly the amount of negative charge to balance with the positive charge, and result in a perfectly neutral atom.
The distance between the nucleus and the outermost electron is 1 Angstrom = 10^-8 cm.
All other electrons balance with all protons except one, and the remaining electron detects the electric field of the proton only 1 A(o) away.
The electric potential = 14.4 V
U = qV
because charge is negative, so is potential energy at 14.4eV, this must be overcome to remove an electron from an atom:
If an atom and a 100,000 V vandegraph fight over an electron the atom will win. This is not
because of voltage, but force. The derivative of potential energy.
The force of the atom is 100,000 times stronger than that of the Van de Graaff.
In lightning, the molecules of air are momentarily ionized leaving a gas of positive molecular ions and negative electrons called a plasma. The electric force between ions and electrons causes them to recombine into neutral matter giving off excess energy in the form of light.
In a neon light, the process is slowed to a continuous glow, but the electric field in a neon light cannot ionize matter.
The neon light and Van de Graaff generator ionize air through collisions that contains not electric force, but a few accidental electrons that hit other molecules. If the electric field is great enough, thus increasing acceleration and the distance between atoms is large enough, the electron can build enough energy to knock another electron off an atom. This causes a chain reaction due to higher acceleration and a spark.
The force of electricity depends on both voltage and charge. Voltage, energy, and force hold the universe together.
Lesson 30 Capacitance and Potential
In 1745, Pieter van Musschenbroek, wanted to make an electric field solution and developed the Leyden jar.
Benjamin Franklin interpreted the Lyden jar and developed an electric theory concerning charge.
In the vacinity of a positive charge, the electric force repels a positive test charge, and an external force is needed to push the charge closer doing work against the electrical force, a positive force (work) if the component does work that is opposite to the electric force.
dW = -F dr
It is known as negative work if it has a component along the force and no work at all if the motion is perpendicular to the electric force.
The net work is found by
integral (dw) = integral (-F dr)
delta (w) = -integral (F dr)
The net work is delta (U) or the change in potential energy of the test charge.
delta (U) = -integral ( F dr)
F = qE
The electric force is the charge multiplied by the electric field.
delta (U) = q delta (V)
delta (V) = -integral (E dr) or the change in electric potential concerning only the path of the charge through the field. it is measured in volts.
Before the electric field, Franklin theorized the electric atmosphere where all objects contain electrical fluid, where objects with too much fluid have a positive charge and objects with too little fluid have a negative charge. Franklin understood that electric charge in never created nor destroyed, but flows from one object to the next.
All objects with a net electrical charge produce an electricl field. If objects contain both positive and negative charges, the electric field exists, but is small in nature, and renders the object with a neutral charge. Inside metals, there is not static electricity because all the charged atoms of the metal are attracted to the surface and prevent further movement.
positive charge: >U
negative charge: <U
where q is proportional to V
A battery can create an electric field where -- as electricity flows between two conductors -- the difference in potential energy is equivalent to the voltage of the battery, and creates an electric field.
q = CV
The charge transfered is proportional to the voltage applied, and the constant of proportionality is C (capacitance).
Franklin revolutionized physics by discovering that electric force is neither created nor destroyed, but transfered from source to source according to the electric charge.
A capacitor can be made with any two pieces of metal. A parallel plate capacitor with two sheets of opposite charge create an electric field between themselves, with the total amount of voltage proportional to distance between the two plates. A parallel plate capacitor was present within Leyden jars.
Benjamin Franklin interpreted the Lyden jar and developed an electric theory concerning charge.
In the vacinity of a positive charge, the electric force repels a positive test charge, and an external force is needed to push the charge closer doing work against the electrical force, a positive force (work) if the component does work that is opposite to the electric force.
dW = -F dr
It is known as negative work if it has a component along the force and no work at all if the motion is perpendicular to the electric force.
The net work is found by
integral (dw) = integral (-F dr)
delta (w) = -integral (F dr)
The net work is delta (U) or the change in potential energy of the test charge.
delta (U) = -integral ( F dr)
F = qE
The electric force is the charge multiplied by the electric field.
delta (U) = q delta (V)
delta (V) = -integral (E dr) or the change in electric potential concerning only the path of the charge through the field. it is measured in volts.
Before the electric field, Franklin theorized the electric atmosphere where all objects contain electrical fluid, where objects with too much fluid have a positive charge and objects with too little fluid have a negative charge. Franklin understood that electric charge in never created nor destroyed, but flows from one object to the next.
All objects with a net electrical charge produce an electricl field. If objects contain both positive and negative charges, the electric field exists, but is small in nature, and renders the object with a neutral charge. Inside metals, there is not static electricity because all the charged atoms of the metal are attracted to the surface and prevent further movement.
positive charge: >U
negative charge: <U
where q is proportional to V
A battery can create an electric field where -- as electricity flows between two conductors -- the difference in potential energy is equivalent to the voltage of the battery, and creates an electric field.
q = CV
The charge transfered is proportional to the voltage applied, and the constant of proportionality is C (capacitance).
Franklin revolutionized physics by discovering that electric force is neither created nor destroyed, but transfered from source to source according to the electric charge.
A capacitor can be made with any two pieces of metal. A parallel plate capacitor with two sheets of opposite charge create an electric field between themselves, with the total amount of voltage proportional to distance between the two plates. A parallel plate capacitor was present within Leyden jars.
Lesson 29 The Electric Field
Michael Faraday developed the idea of the electric field as lines of constant electric force radiating everywhere throughout space (known as the field theory).
Charles Augustine Coulomb:
F(e) = K(e) (q1q2/r^2) r^
where the electric force is inversely proportional to the square of the distance between two charges.
The Universal Law of Gravitation also follows a similar principle where F(g) = -G (m1m2/r^2)r^. This law led to the development of the theory and phrase "action at a distance" where bodies such as the earth and sun directly apply force to one another over copius kilometers.
F(e) = K(e) (q1q2/r^2) r^
F(g) = -G (m1m2/r^2)r^
F(m) = K(m) (p1p2/r^2)r^
All these laws have a force that decreases with the square of the distance.
The inverse square law is related to a simple geometric characteristic of space, known as flux, where intensity alpha = 1/r^2 describing the radiating light of the sun.
Faraday set out to solve the scientific mystery of why a compass needle spins to a perpendicular position from an electric charge, and developed an electric motor.
Anywhere in the vacinity of an electric charge a small test charge experiences a force. If it is due to only one charge the pattern of forces detected by the test charge is simple where similar forces repel and opposite forces attract.
The pattern of forces is present in a space as a field and can be expressed mathematically
F = sum (K(e) (qqi/ri^2) r^i)
The force that acts on a test charge at each point in space is equal to the test charge times a quantity of the other charges. That quantity is the electric field F = qE E= sum (K(e) (qqi/ri^2) r^i)
The 1/r^2 force between electric charges suggest that the force must be applied by something radiating outward from charges, something which like light from the sun never stops and never ends in space. These forces take characteristics of lines that never cross or angle. This electric field force is stronger near charges where lines (vectors) are close together and weak where the lines are far apart.
Gauss developed the mathematics of the Electric field theory through Gauss's Law:
for any closed surface total flux is proportional to the net electric charge inside. If there's no net charge inside a surface, any positive flux outward through it, must be balanced by inward, negative flux.
This law applies to light, gravitational fields, magnetic fields, and electric fields.
An electric field passing through a conductor forces the electrons to flow until they pile up at the surface repelling further motion of electron. The electric fiel inside any conductor becomes equal to zero when electrostatic equilibrium is established. Therefore, a closed surface inside the conductor has no flux through it, so the net charge inside must be zero, bu there can be charge at the surface. No matter what is outside, the surface charge makes the electric field inside equal to zero.
A metal box of any kind can keep out an electric field, known as the Faraday cage. This explains why drivers lose radio reception when passing through tunnels or bridges.
Gauss's law proves the theory of the center of mass.
Maxwell worked to express the electric field in mathematical terms.
Charles Augustine Coulomb:
F(e) = K(e) (q1q2/r^2) r^
where the electric force is inversely proportional to the square of the distance between two charges.
The Universal Law of Gravitation also follows a similar principle where F(g) = -G (m1m2/r^2)r^. This law led to the development of the theory and phrase "action at a distance" where bodies such as the earth and sun directly apply force to one another over copius kilometers.
F(e) = K(e) (q1q2/r^2) r^
F(g) = -G (m1m2/r^2)r^
F(m) = K(m) (p1p2/r^2)r^
All these laws have a force that decreases with the square of the distance.
The inverse square law is related to a simple geometric characteristic of space, known as flux, where intensity alpha = 1/r^2 describing the radiating light of the sun.
Faraday set out to solve the scientific mystery of why a compass needle spins to a perpendicular position from an electric charge, and developed an electric motor.
Anywhere in the vacinity of an electric charge a small test charge experiences a force. If it is due to only one charge the pattern of forces detected by the test charge is simple where similar forces repel and opposite forces attract.
The pattern of forces is present in a space as a field and can be expressed mathematically
F = sum (K(e) (qqi/ri^2) r^i)
The force that acts on a test charge at each point in space is equal to the test charge times a quantity of the other charges. That quantity is the electric field F = qE E= sum (K(e) (qqi/ri^2) r^i)
The 1/r^2 force between electric charges suggest that the force must be applied by something radiating outward from charges, something which like light from the sun never stops and never ends in space. These forces take characteristics of lines that never cross or angle. This electric field force is stronger near charges where lines (vectors) are close together and weak where the lines are far apart.
Gauss developed the mathematics of the Electric field theory through Gauss's Law:
for any closed surface total flux is proportional to the net electric charge inside. If there's no net charge inside a surface, any positive flux outward through it, must be balanced by inward, negative flux.
This law applies to light, gravitational fields, magnetic fields, and electric fields.
An electric field passing through a conductor forces the electrons to flow until they pile up at the surface repelling further motion of electron. The electric fiel inside any conductor becomes equal to zero when electrostatic equilibrium is established. Therefore, a closed surface inside the conductor has no flux through it, so the net charge inside must be zero, bu there can be charge at the surface. No matter what is outside, the surface charge makes the electric field inside equal to zero.
A metal box of any kind can keep out an electric field, known as the Faraday cage. This explains why drivers lose radio reception when passing through tunnels or bridges.
Gauss's law proves the theory of the center of mass.
Maxwell worked to express the electric field in mathematical terms.
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