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.