TABLE OF CONTENTS 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) |  |
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) |  |
The total...
