A cable carrying a direct current is buried in a wall which stands in a north-south plane. A horizon

Question

A cable carrying a direct current is buried in a wall which stands in a north-south plane. A horizontal compass needle on the west side of the wall is found to point towards south instead of north. The coil is laid\

Professor PC Thomas Classes · Answer

Case I : Current upward\ On the eastern side both $B$ and $B_{H}$ are in the same direction ie towards the north. So no chance of a null point on the eastern side. But on the western side $B$ and $B_{H}$ are opposite. At the point $N, B= B_{H}$. Therefore it is a null point. Between the null point and the conductor $B>B_{H}$. Therefore the net field is southwards. So a pivoted needle will have its north pole pointing south when placed between the conductor and the null point.\ Case II ; If the current is downward the situation gets reversed. The null point will be on the eastern side. At the null point $\mathrm{B}=\mathrm{B}_{\mathrm{H}}$\ $\frac{\mu_{0} \mathrm{I}}{2 \pi \mathrm{r}}=\mathrm{B}_{\mathrm{H}}$\