Question 31:
moderateA long straight wire of radius $a$ carries a steady current $I$. The current is uniformly distributed over its cross-section. The ratio of the magnetic fields $B$ and $B’$ at radial distances $\frac{a}{2}$ and $2a$ respectively, from the axis of the wire is:
(2016-1)
The magnetic field inside the wire at distance $r = a/2$ is given by $B = \frac{\mu_0 I r}{2\pi a^2}$. The magnetic field outside at $r' = 2a$ is $B' = \frac{\mu_0 I}{2\pi r'}$. Evaluating both gives equal magnitudes, so the ratio $B / B'$ is equal to $1$.