Question

A current I flows in a straight wire bent in the shape of a quarter ring of radius $R$ as shown in figure. The magnetic field induction $(B)$ at point $O$ is

• A. $\frac{\mu_{0} I}{4 R}$
• B. $\frac{\mu_{0} I}{8 R}$
• C. $\frac{\mu_{0} I}{2 R}$
• D. $\frac{\mu_{0} I}{6 R}$

Answer 1

Answer: (B)

Magnetic field at centre of a complete current carrying circular loop is
$B=\frac{\mu_{0} I}{2 R}$

For one quarter of loop,
$B=\frac{1}{4} \times \frac{\mu_{0} I}{2 R}=\frac{1}{8}\left(\frac{\mu_{0} I}{R}\right) T$