Question

A long straight wire of radius $ R $ carries a steady current $ I $ . The current is uniformly distributed across its cross-section. The ratio of magnetic field at $ R/2 $ and $ 2R $ is

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

Answer 1

Answer: (D)

The magnetic field inside the current carrying wire
$B$ at $\frac{R}{2}$ distance,
$B_{R/2} =\frac{ \mu_{0} i}{2 \pi R^{2}} \times \frac{R}{2} =\frac{ \mu_{0}i}{4 \pi R} $
At distance, $2R$
$ B_{2R} = \frac{\mu_{0}i}{2 \pi\left(2R\right)} = \frac{\mu_{0}i}{4 \pi R} $
$ \therefore \frac{B_{R/2}}{B_{2R}} = 1 : 1 $