Question

A pair of stationary and infinitely long bent wires is placed in the x-y plane as shown in figure. Each wire carries current of $10A$. Segments $L$ and $M$ are along the x-axis.Segments $P$ and $Q$ are parallel to the y-axis such that $OS=OR=0.02m$. Find the magnitude and direction of the magnetic induction at origin $O$ in the form of $x\times {10}^{-4}$. What is x.

Answer 1

As point $O$ is along the length of segments $L$ and $M$, so the field at $O$ due to these segments will be zero.

Also, point $O$ is near one end of a long wire.
The resultant field at $O$, $B_R=B_P+B_Q$, this field willbe into the plane paper.
$\Rightarrow B_R=\frac{{\mu }_0}{4\pi }\frac{I}{RO}+\frac{{\mu }_0}{4\pi }\frac{I}{SO}$
But, $RO=SO=0.02m$
Hence, $B_R=2\times \frac{{\mu }_0}{4\pi }\times \frac{10}{0.02}=2\times {10}^{-7}\frac{10}{0.02}={10}^{-4}Wb$ $m^{-2}$