Question

A straight conductor of length $ l $ carrying a current $ I, $ is bent in the form of a semicircle. The magnetic field (in tesla) at the centre of the semicircle is

• A. $ \frac{{{\pi }^{2}}I}{l}\times {{10}^{-7}} $
• B. $ \frac{\pi I}{l}\times {{10}^{-7}} $
• C. $ \frac{\pi I}{{{l}^{2}}}\times {{10}^{-7}} $
• D. $ \frac{\pi {{I}^{2}}}{l}\times {{10}^{-7}} $

Answer 1

Answer: (A)

Radius, $r=\frac{1}{\pi}$
Magnetic field at the centre, $B=\frac{\mu_{0} I}{4 r}$
$=\frac{4 \pi \times 10^{-7} \times I}{4 \times \frac{l}{\pi}}$
$=\frac{\pi^{2} I \times 10^{-7}}{l}$