Question

Two concentric coils of $10$ turns each are placed in the same plane. Their radii are $20cm$ and $40cm$ and carry $0.2A$ and $0.3A$ current respectively in opposite directions. The magnetic induction (in $tesla$ ) at the center is

• A. $\frac{3}{4}{\mu }_0$
• B. $\frac{5}{4}{\mu }_0$
• C. $\frac{7}{4}{\mu }_0$
• D. $\frac{9}{4}{\mu }_0$

Answer 1

Answer: (B)

Two coils carry currents in opposite directions, hence net magnetic field at centre will be difference of the two fields.
$ie,B_{net}=\frac{{\mu }_0}{4\pi }.2\pi N\left[\frac{i_1}{r_1}-\frac{i_2}{r_2}\right]$
$=\frac{10{\mu }_0}{2}\left[\frac{0.2}{0.2}-\frac{0.3}{0.4}\right]$
$=\frac{5}{4}{\mu }_0$