Moving Charges and Magnetism - Result Question 32
33. A 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 $B^{\prime}$, at radial distances $\frac{a}{2}$ and $2 a$ respectively, from the axis of the wire is :
[2016]
(a) $\frac{1}{4}$
(b) $\frac{1}{2}$
(c) 1
(d) 4
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Answer:
Correct Answer: 33. (c)
Solution:
- (c) For points inside the wire i.e., $(r \leq R)$
Magnetic field $B=\frac{\mu_0 I r}{2 \pi R^{2}}$
For points outside the wire $(r \geq R)$
Magnetic field, $B^{\prime}=\frac{\mu_0 I}{2 \pi R}$
$\therefore \quad \frac{B}{B^{\prime}}=\frac{\frac{\mu_0 I(a / 2)}{2 \pi a^{2}}}{\frac{\mu_0 I}{2 \pi(2 a)}}=1: 1$
