Question

Two concentric circular coils of 10 turns each are situated in the same plane. Their radii are 20 cm and 40cm and they carry currents of 0.2A and 0.3A respectively in opposite directions. If ${\mu }_0$ is permeability of vacuum, then the magnetic field in$Wb/m^2$at the common centre is

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

Answer 1

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

$B=\frac{{\mu }_{0}10}{2}[\frac{i_1}{r_1}-\frac{i_2}{r_2}]B=\frac{{\mu }_{0}10}{2}[\frac{0.2}{20}-\frac{0.3}{40}]{10}^2=5{\mu }_0[1-\frac{3}{4}]=\frac{5{\mu }_0}{4}$