Question

A straight wire of finite length carrying current $I$ subtends an angle of $60^{\circ}$ at point $P$ as shown. The magnetic field at $P$ is

• A. $\frac{\mu_{0} I}{2 \sqrt{3} \pi x}$
• B. $\frac{\mu_{0} I}{2 \pi x}$
• C. $\frac{\sqrt{3} \mu_{0} I}{2 \pi x}$
• D. $\frac{\mu_{0} I}{3 \sqrt{3} \pi x}$

Answer 1

Answer: (A)

$B=\frac{\mu_{0} I}{4 \pi x \cos 30^{\circ}}\left[\sin 30^{\circ}+\sin 30^{\circ}\right]$
$B=\frac{\mu_{0} I}{4 \pi x\left(\frac{\sqrt{3}}{2}\right)}\left(\frac{1}{2}+\frac{1}{2}\right)$
$=\frac{\mu_{0} i}{2 \sqrt{3} \pi x}$