Question

A current I flows in a circular arc of radius R, which subtends an angle $\frac{\pi }{6}$ radian at the center. The magnetic induction B at the center is

• A. $\frac{{I\mu }_0}{4R}$
• B. $\frac{{I\mu }_0}{2R}$
• C. $\frac{{I\mu }_0}{24R}$
• D. $\frac{{I\mu }_0}{12R}$

Answer 1

The correct option is C $\frac{{I\mu }_0}{24R}$

The correct option is C.

Given,

$Current=I,Rdius=R,aAngle=\frac{\pi }{6}$

So, For a coil of turns,

Magnetic field is $B=\frac{{\mu }_{0}In}{6R}$

Here $n=\frac{1}{4}$

$\theta =\frac{\pi }{6}$

Therefore,

$B=\frac{{\mu }_{0}I}{24R}$