Chapter 8: Magnetic Field Inside the Current Source

Illustration 2

Unlike the electric field, the magnetic field does not vanish in conductors. Inside a conductor through which current flows, there is some nonzero magnetic field. This is well seen in Figure 1, which shows the magnetic field of a single wire with uniform current distribution.

Similarly to the uniformly charged cylinder and its electric field, the magnetic field in a cylinder with uniform current density increases linearly with the radial distance from the center of the wire, i.e., . Once the observation point crosses over to free space, the field strength starts to decrease as —same as the field of an infinitely long wire with current. This behavior is illustrated in Figure 2.

Figure 3 shows the magnetic field in a coaxial-type line with rather thick inner wire and shield. Observe the behavior of the field magnitude both in the inner wire, where it increases linearly, and the outer shield, where it decreases linearly.

 
Figures (click to enlarge)
Figure 1

Figure 2

Figure 3

Figure 1: The magnetic (H-field) streamlines inside and outside a single thick wire.

 

Figure 2: The H-field magnitude inside and outside the thick wire with uniform current density.

 

Figure 3: The H-field magnitude inside and outside the thick conductors of a coaxial line.