5.1 BIOT-SAVART LAW

While preparing a lecture demonstration in 1820, rsted noticed that current flowing through a wire deflected a nearby compass needle. After further investigations, he published his discovery that an electric current flowing through a wire gives rise to a magnetic field.

The strength of the electric field is determined by the magnitude the force exerted on a hypothetical test charge according to F = q E. In a similar way, the magnetic field B may be determined by the torque ? exerted on a magnetic dipole with dipole moment

(5.1)

The continuity equation

(5.2)

is a statement of charge conservation. Magnetostatic fields are produced by steady state currents that are not changing in time so that we have

(5.3)

The field d B produced by a current dipole I d ? located at the position r' decreases as the inverse square of the distance from the current source according to

(5.4)

This expression is analogous to the Coulomb's law describing the field produced by a single point charge. The Biot-Savart law gives the magnetic field at a position r resulting from a continuous current distribution J( r')

(5.5)

5.2 AMPERE'S LAW

Ampere's law relates the line integral of magnetic field around any closed path ? surrounding a wire carrying a total current I as shown in Figure 5.1.

(5.6)

Figure 5.1: Amperian loop ? surrounding a wire carrying a current I.

The total...