Question

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

• A. $\frac{{\mu }_{0}i}{R}$
• B. $\frac{2{\mu }_{0}i}{R}$
• C. $\frac{{\mu }_{0}i}{2R}$
• D. $\frac{3{\mu }_{0}i}{8R}$

Answer 1

The correct option is D $\frac{3{\mu }_{0}i}{8R}$


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

Magnetic field at the centre of a current carrying circular arc is given by

$B=\frac{{\mu }_{0}i}{2R}\times \frac{\theta }{2\pi }$

$B=\frac{{\mu }_{0}i}{2R}\times \frac{3\pi /2}{2\pi }(\because \theta =3\pi /2)$

$\therefore B=\frac{3}{8}\frac{{\mu }_{0}i}{R}$

Therefore, the correct option is $\left(d\right)$.