The figure shows a long cylindrical straight wire of radius $a$ carrying steady current ($I$). The current ($I$) is uniformly distributed across the cross-section of the wire. The ratio of the magnetic fields at points $r =\frac{a}{3}$ and $r =\frac{a}{2}$ respectively is: Here $r$ is the distance of point from the axis of cylinder.

2 : 3

The correct answer is Option (1) → 2 : 3

Inside a uniformly current-carrying wire of radius $a$, the magnetic field at distance $r

$B = \frac{\mu_0 I r}{2\pi a^2}$

Thus, $B \propto r$ (inside the conductor).

For $r_1 = \frac{a}{3}$ and $r_2 = \frac{a}{2}$:

$\frac{B_1}{B_2} = \frac{r_1}{r_2} = \frac{a/3}{a/2} = \frac{2}{3}$

∴ The ratio of magnetic fields is $2 : 3$.