Question

A solid conductor with radius a is supported by insulating disks on the axis of a conducting tube with inner radius b and outer radius c (see figure). The central conductor and tube carry equal currents I in opposite directions. The currents are distributed uniformly over the cross sections of each conductor.

(a) Derive an expression for the magnitude of the magnetic field at points outside the central, solid conductor, but inside the tube (a < r < b). (Use any variable or symbol stated above along with the following as necessary:)

(b) Derive an expression for the magnitude of the magnetic field at points outside the tube (r > c). (Use any variable or symbol stated above as necessary.)

Answer 1

a) \(B\) at \((a

Applying Ampere's law, \(\int B \cdot d l=\mu_{0} I\)

\(B \int d l=\mu_{0} I\)

\(B * 2 \pi r=\mu_{0} I\)

\(\mathbf{B}=\frac{\mu_{0} \mathbf{I}}{2 \pi \mathbf{r}}=\frac{2 * 10^{-7} * I}{r}\) Tesla

[b]

\(\mathrm{B}\) at \((r>\mathrm{c})\)

Applying Ampere's law, \(\int B \cdot d l=\mu_{0} I\)

\(B \int d l=\mu_{0} I\)

\(B * 2 \pi r=\mu_{0}[I-I]\)

B=0T