Question

A Coaxial cable consists of a solid inner cylindrical conductor of radius 2 mm and an outer cylindrical shell of inner radius 3 mm and outer radius 3.5 mm. A current of 15 A flows down the inner wire and an equal return current flows in the outer conductor. If we assume that the currents are uniform over the cross section of the conductors, then calculate the magnetic field at a radius of 2.5 mm (use ampere's law) [A] 2.4 mT [B] 2.1 uT [C] 3.2 uT [D] 1.2 mT [E] 0.

Answer 1

Using Ampere's law,
B * 2r = _o * I_enclosed
Where r = 2.5 mm = 2.5 * 10^-3 m
Here I_enclosed = 15 A since the inner conductor is fully inside the radius r and the outer shell is completely outside r.

B = [_o * I_enclosed] / 2r
= [4 * 10^-7 * 15] / [2 * 2.5 * 10^-3]
= 1.2 * 10^-3 T
= 1.2 mT (Option D)