Question

A current flows in a circular arc of wire whose radius is $R$, which subtends an angle $\frac{3\pi }{2}$ radian at its centre. The magnetic field $B$ at the centre is

• A. $\frac{{\mu }_0}{2R}$
• B. $\frac{3{\mu }_0}{8R}$
• C. $\frac{{\mu }_0}{18R}$
• D. $\frac{{\mu }_0}{36R}$

Answer 1

The correct option is B $\frac{3{\mu }_0}{8R}$

$Given:$ $\theta$ = $\frac{3\pi }{2}$

$Solution:$ The magnetic induction due to a circular coil is given by

$B=$ $\frac{\theta {\mu }_o}{4\pi R}$

Where $\theta$ is the angle subtended by the arc at its centre then putting $\theta$ = $\frac{3\pi }{2}$

then,we get

$B=$ $\frac{3{\mu }_o}{8R}$

$So,the$ $correct$ $option:B$