Two concentric circular coils of 10 turns each are situated in the same plane. Their radii are $20…

Two concentric circular coils of 10 turns each are situated in the same plane. Their radii are $20 \mathrm{~cm}$ and $40 \mathrm{~cm}$ and they carry respectively $0.2 \mathrm{~A}$ and $0.3 \mathrm{~A}$ current in opposite direction. The magnetic field at the centre is ( $\mu_0=4 \pi \times 10^{-7}$ SI units)
  1. $4 \pi \times 10^{-7} \mathrm{~T}$
  2. $5 \pi \times 10^{-7} \mathrm{~T}$
  3. $2 \pi \times 10^{-5} \mathrm{~T}$
  4. $7 \pi \times 10^{-6} \mathrm{~T}$

Solution

$\begin{aligned} \mathrm{B}_{\text {net }} & =\frac{\mu_0 \mathrm{n}_1 \mathrm{I}_1}{2 \mathrm{r}_1}-\frac{\mu_0 \mathrm{n}_2 \mathrm{I}_2}{2 \mathrm{r}_2} \\ & =\frac{10 \mu_0}{2}\left[\frac{0.2}{0.2}-\frac{0.3}{0.4}\right] \\ & =5 \times 4 \pi \times 10^{-7} \times 0.25 \\ & =5 \pi \times 10^{-7} \mathrm{~T}\end{aligned}$ :

Asked in: MHT CET 2023 (12 May Shift 2)

Practice more Magnetic Fields due to Electric Current questions on Aicharya