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

The correct option is A $\frac{{\mu }_{0}I}{2\sqrt{3}\pi x}$

$\text{B}=\frac{{\mu }_0}{4\pi }\frac{\text{I}}{\text{R}}(\sin {\varphi }_1+\sin {\varphi }_2)$

$\text{B}=\frac{{\mu }_0}{4\pi }\frac{\text{I}}{x\cos {30}^o}(\sin {30}^o+\sin (-{30}^o\left)\right)$

$\text{B}=\frac{{\mu }_{0}I}{2\sqrt{3}\pi }$

Hence, magnetic field is $\frac{{\mu }_{0}I}{2\sqrt{3}\pi x}$