A solid cylindrical conductor is supported by insulating disks on the axis of a

Question

A solid cylindrical conductor is supported by insulating disks on the axis of a conducting tube with outer radius Ra = 6.65 cm and inner radius Rb = 4.65 cm . (Figure 1) The central conductor and the conducting tube carry equal currents of I = 2.05 A in opposite directions. The currents are distributed uniformly over the cross sections of each conductor. What is the value of the magnetic field at a distance r = 5.50 cm from the axis of the conducting tube?

What is the value of the magnetic field at a distance r = 5.50 cm from the axis of the conducting tube? Recall that ?0=4?×10?7 T?m/A.

Explanation / Answer

Here ,

Ra = 6.65 cm

Rb = 4.65 cm

I = 2.05 A

r = 5.5 cm

let the magnetic field is B

Using Amphere's circuital law

B * 2pi * r = u0 * I * (r^2 - Ra^2)/(Rb^2 - Ra^2)

B * 2pi * 0.055 = 4pi *10^-7 * 2.05 * (5.5^2 - 4.65^2)/(6.65^2 - 4.65^2)

solving for B

B = 2.85 *10^-6 T

the magnetic field is 2.85 *10^-6 T

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