Question

Two identical circular loops, $P$ and $Q$, each of radius $r$ and carrying equal currents are kept in the parallel planes having a common axis passing through $O$. The direction of current in $P$ is clockwise and in $Q$ is anti-clockwise as seen from $O$ which is equidistant from the loops $P$ and $Q$. Find the magnitude of the net magnetic field at $O$.

Answer 1

Magnetic field at O due to P=$\left|\overrightarrow{B_P}\right|=\frac{{\mu }_0{r}^{2}I}{2(r^2+r^2{)}^{3/2}}=\frac{{\mu }_{0}I}{4\sqrt{2}r}$ pointing towards P.

Magnetic field at O due to Q=$\left|\overrightarrow{B_Q}\right|=\frac{{\mu }_0{r}^{2}I}{2(r^2+r^2{)}^{3/2}}=\frac{{\mu }_{0}I}{4\sqrt{2}r}$ pointing towards P.
Hence magnetic field at point O=$\overrightarrow{B_Q}+\overrightarrow{B_P}=\frac{{\mu }_{0}I}{2\sqrt{2}r}$ towards P.