Question

Two concentric coils of $10$ turns each are situated in the same plane. Their radii are $20cm$ and $40cm$ and they carry $0.2$ and $0.3$ $A$ current respectively in opposite directions. The magnetic field in $Wb/m^2$ at the centre is :

• A. $\frac{7{\mu }_0}{8}$
• B. $\frac{3{\mu }_0}{8}$
• C. $\frac{{\mu }_0}{8}$
• D. $\frac{5{\mu }_0}{4}$

Answer 1

Answer: (D)

$\frac{5{\mu }_0}{4}$

Magnetic field due to circular coil of n turns is given by,
$B_1=\frac{n_1{\mu }_0{i}_1}{2r_1}$=$\frac{{\mu }_0\times 10\times 0.2}{2\times 20}$=$\frac{2{\mu }_0\times 100}{40}$
$B_2=\frac{n_2{\mu }_0{i}_2}{2r_2}$=$\frac{3{\mu }_0\times 100}{80}$
$B_1-B_2=\frac{100{\mu }_0}{80}$$=\frac{5{\mu }_0}{4}$