Question

Two very long straight wires are set parallel to each other. Each carries a current $I$ in the same direction and the separation between them is $2r$. The intensity of magnetic field at point $P$ as shown in figure is ______

• A. $\frac{3}{8}\frac{{\mu }_{0}I}{\pi r}$
• B. $\frac{{2\mu }_{0}I}{\pi r}$
• C. $\frac{2}{3}\frac{{\mu }_{0}I}{\pi r}$
• D. $\frac{{\mu }_{0}I}{2\pi r}$

Answer 1

Answer: (C)

$\frac{2}{3}\frac{{\mu }_{0}I}{\pi r}$

Magnetic field due to first wire $B_1=\frac{{\mu }_{0}i}{2\pi r}$
Magnetic field due to second wire $B_2=\frac{{\mu }_{0}i}{6\pi r}$
Net magnetic field at $P,B=B_1+B_2$
$B=\frac{{\mu }_{0}I}{2\pi r}+\frac{{\mu }_{0}I}{6\pi r}=\frac{2}{3}\frac{{\mu }_{0}i}{\pi r}$