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  4. 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 (a/2) and 2a respectively, from the axis of the wire is :

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Q. 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 :

NEETNEET 2016Moving Charges and Magnetism

Solution:

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 $