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.