Question

Consider a co-axial cable which consists of an inner wire of radius ‘a’, surrounded by an outer shell, of inner and outer radii b and c, respectively. The inner wire carries a current I and the outer shell carries an equal and opposite current. The magnetic field at a distance x from the axis, where b < x < c, is

(1) \(\frac{μ_0I(c^2-b^2)}{2\pi x (c^2 -a^2)}\)

(2) \(\frac{μ_0I(c^2-x^2)}{2\pi x (c^2 -a^2)}\)

(3) \(\frac{μ_0I(c^2-x^2)}{2\pi x (c^2 -b^2)}\)

(4) \(\frac{μ_0I(c^2-b^2)}{2\pi x (c^2 -x^2)}\)

Answer 1

 (3) \(\frac{μ_0I(c^2-x^2)}{2\pi x (c^2 -b^2)}\)

Consider an amperian loop of radius ‘x’ (b < x < c) 

Threaded current I’, by this amperian loop, is