Question

Magnetic field at point P at a distance d from vertex of infinite wire carrying current $i$ as shown in figure is

• A. $\frac{{\mu }_0}{2\pi }\frac{i}{d}$
• B. $\frac{{\mu }_{0}i}{4\pi d}(1-\sqrt{3})$
• C. $\frac{{\mu }_0}{4\pi }\frac{i}{d}(2-\sqrt{3})$
• D. $\frac{{\mu }_0}{\pi }\frac{i}{d}$

Answer 1

The correct option is C $\frac{{\mu }_0}{4\pi }\frac{i}{d}(2-\sqrt{3})$

By $\Delta ABPsin30=\frac{PB}{d}\Rightarrow PB=\frac{d}{2}$
For wire $Al\Rightarrow B_1=\frac{{\mu }_0}{4\pi }\frac{i}{\frac{d}{2}}[\sin \frac{\pi }{2}-\sin \alpha ](\alpha ={60}^{\circ })$