Question

Two concentric coils of $10$ turns each are placed in the same plane. Their radii are $20 \, cm$ and $40 \, cm$ and carry $0.2 \, A$ and $0.3 \, A$ 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.
$ie, \, B_{n e t}=\frac{\mu _{0}}{4 \pi } \, . \, 2\pi N\left[\frac{i_{1}}{r_{1}} - \frac{i_{2}}{r_{2}}\right]$
$=\frac{10 \mu _{0}}{2}\left[\frac{0.2}{0.2} - \frac{0.3}{0.4}\right]$
$=\frac{5}{4}\mu _{0}$