Question

A long straight wire of radius a carries a steady current I. The current uniformly distributed over its cross-section. The ratio of the magnetic fields B and B', at radial distance $\frac{a}{2}$ and 2a respectively, from the axis of the wire is :

• A. $\frac{1}{2}$
• B. 1
• C. 4
• D. $\frac{1}{4}$

Answer 1

Answer: (B)

1

Answer 2

For points inside the wire
$B = \frac{\mu_0 I r}{2 \pi R^2} (r \le R)$
For points outside the wire
$B = \frac{\mu_0 I}{2 \pi r} (r \ge R)$
according to the question
$\frac{B}{B'} = \frac{\frac{\mu_0 I (a /2)}{2 \pi a^2}}{\frac{\mu_0 I }{2 \pi(2a)}} = 1 : 1$