Question

Two concentric circular coils of ten turns each are situated in the same plane. Their radii are $20cm$ and $40cm$ and they carry respectively $0.2A$ and $0.3A$ currents in opposite direction. The magnetic field in tesla at the centre is

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

Answer 1

Answer: (D)

Magnetic field at the centre of circular coil consists of N turns and radius r carrying current i
is given by $B=\frac{{\mu }_{0}2\pi Ni}{4\pi r}$
For first coil, $B_1=\frac{{\mu }_{0}2\pi N_1{i}_1}{4\pi r_1}$
$=\frac{{\mu }_0\times 10\times 0.2}{2\times 0.2}$
For second coil, $B_2=\frac{{\mu }_{0}2\pi N_2{i}_2}{4\pi r_2}=\frac{{\mu }_0\times 10\times 0.3}{2\times 0.4}$
The resultant magnetic field at the centre of the concentric coil is
$B=B_1-B_2=\frac{{\mu }_0\times 10\times 0.2}{2\times 0.2}-\frac{{\mu }_0\times 10\times 0.3}{2\times 0.4}$
$=\frac{10{\mu }_0}{2}\left[1-\frac{3}{4}\right]=\frac{10{\mu }_0}{2}\left(\frac{1}{4}\right)=\frac{5{\mu }_0}{4}$