Question

Two concentric circular coils of $10$ turns each are situated in the same plane. Their radii are $20$ cm and $40$ cm and carry currents of $0.2$ A and $0.3$ A respectively in opposite directions. The net magnetic induction field at their common centre is

• A. $\frac{35{\mu }_0}{4}$
• B. $\frac{5{\mu }_0}{4}$
• C. $\frac{7{\mu }_0}{8}$
• D. $\frac{{\mu }_0}{80}$

Answer 1

The correct option is B $\frac{5{\mu }_0}{4}$

Two coils carrying current in opposite direction,

hence net magnetic field at centre will difference of the two fields.

i.e. $B_{net}=\frac{{\mu }_0}{4\pi }.2\pi N[\frac{N{i}_1}{r_1}-\frac{i_2}{r_2}]$

$=\frac{10{\mu }_0}{2}[\frac{0.2}{0.2}-\frac{0.3}{0.4}]=\frac{5}{4}{\mu }_0$