Question

Two identical circular loops, $P$ and $Q$, each of radius $r$ and carrying currents $1$ and $21$ respectively are lying in parallel planes such that they have a common axis. The direction of current in both the loops is clockwise as seen from $O$ which is equidistance from the both loops. Find the magnitude of the net magnetic field at point $O$.

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