Q. A current of $i$ ampere flows in a circular area of wire which subtends an angle of $(3\pi/2)$ radian at its centre, whose radius is $R.$ The magnetic induction $B$ at the centre is
A) $\mu_{0}\ i/R$
B) $\mu_{0}\ i/2R$
C) $2\mu_{0}\ i/R$
D) $3\mu_{0}\ i/8R$
Explanation
(d) For a loop, magnetic induction at centre,
$B = \frac{\mu_{0}}{4\pi} \times \frac{2\pi i}{R}$
When loop subtends angle $\theta$ at centre, then
$B = \frac{\mu_{0}}{4\pi} \times \frac{\theta i}{R}$
In the given problem, $\theta = 3\pi/2$
$\therefore b = \frac{\mu_{0}}{4\pi} \times \frac{3\pi}{2} \times \frac{i}{R} = \frac{3\mu_{0}i}{8R}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.