Question

Two concentric circular coils of ten turns each are situated in the same plane. Their radii are $20\, cm$ and $40\, cm$ and they carry respectively $0.2\, A$ and $0.3\, A$ 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, $B_{1}=\frac{\mu_{0} 2\pi N_{1}i_{1}}{4\pi r_{1}}$
$=\frac{\mu_{0}\times10\times0.2}{2\times0.2}$
For second coil, $B_{2}=\frac{\mu_{0} 2\pi N_{2}i_{2}}{4\pi r_{2}}=\frac{\mu_{0}\times10\times0.3}{2\times0.4}$
The resultant magnetic field at the centre of the concentric coil is
$B=B_{1}-B_{2}=\frac{\mu_{0}\times10\times0.2}{2\times0.2}-\frac{\mu_{0}\times10\times0.3}{2\times0.4}$
$=\frac{10\mu_{0}}{2} \left[1-\frac{3}{4}\right]=\frac{10\mu_{0}}{2}\left(\frac{1}{4}\right)=\frac{5\mu_{0}}{4}$