Question

A long straight wire of circular cross section of radius ҅a᾿ carries a steady current I. The current is uniformly distributed across its cross section. The ratio of magnitudes of the magnetic field at a point a/2 above the surface of wire to that of a point a/2 below its surface is 

(A) 4:1 

(B) 1:1 

(C) 4: 3 

(D) 3 :4

Answer 1

Correct option is : (C) 4: 3

At \(P_2, \ B_2 = \frac{\mu_0I}{2\pi\left(\frac{3a}{2}\right)} = \frac{\mu_0I}{3\pi a}\)

At \(P_1,\ B_1 = \frac{\mu_0(1/4)}{2\pi(a/2)} = \frac{\mu_0I}{4\pi a}\)

\(\therefore\ \frac{B_2}{B_1} = \frac{(\frac{\mu_0I}{3\pi a})}{(\frac{\mu_0I}{4\pi a})}\Rightarrow\frac{B_2}{B_1} = \frac{4}{3}\)