Question

Two parallel wires carrying equal currents in opposite directions are placed at $x=\pm a$ parallel to y-axis with $z=0$. Magnetic field at origin $O$ is $B_1$ and at $P(2a,0,0)$ is $B_2$. Then, the ratio $B_1/B_2$ is

• A. $3$
• B. $1/2$
• C. $1/3$
• D. $2$

Answer 1

The correct option is A $3$

As shown if figure

$\overrightarrow{B_1}=-2\left(\frac{{\mu }_0}{2\pi }\frac{i}{a}\right)\hat{k}=-\frac{{\mu }_{0}i}{\pi a}\hat{k}=$magnetic field at $O$

$\overrightarrow{B_2}=\frac{{\mu }_0}{2\pi }\frac{i}{a}\hat{k}-\frac{{\mu }_0}{2\pi }\frac{i}{3a}\hat{k}=\frac{{\mu }_0}{3\pi }\frac{i}{a}\hat{k}=$ magnetic field at $P$

$\therefore B_1/B_2=3$