Question

A wire carrying current I has the shape as shown in adjoining figure. Linear parts of the wire are very long and parallel to X-axis while semicircular portion of radius R is lying in Y-Z plane. Magnetic field at point O is:(a) $\vec{B}=-\frac{\mu_{0}}{4\pi}\frac{I}{R}(\mu\hat{i}\times 2\hat{k})$(b) $\vec{B}=-\frac{\mu_{0}}{4\pi}\frac{I}{R}(\pi\hat{i}+2\hat{k})$(c) $\vec{B}=\frac{\mu_{0}}{4\pi}\frac{I}{R}(\pi\hat{i}-2\hat{k})$(d) $\vec{B}=\frac{\mu_{0}}{4\pi}\frac{I}{R}(\pi\hat{i}+2\hat{k})$

Answer 1

For Infinite Length -

Parallel wires 1 and 3 are semi-infinite as shown in the figure,

So from the magnetic field at 0 due to them  will be identical to X-axis while a semicircular portion of radius R is lying in Y-Z plane

The magnetic field at 0 due to curved arc in the yz plane is given by

Therefore the Net magnetic field at point O as shown below.