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(B) The magnetic field at the center of a circular coil is given by $B = \frac{\mu_0 N i}{2r}$.Since the two coils carry currents in opposite directio

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$\frac{5}{4} \mu_0$

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(B) The magnetic field at the center of a circular coil is given by $B = \frac{\mu_0 N i}{2r}$.Since the two coils carry currents in opposite directions,the net magnetic field at the center is the difference between the two fields.Given: $N_1 = N_2 = 10$,$r_1 = 0.2 \ m$,$r_2 = 0.4 \ m$,$i_1 = 0.2 \ A$,$i_2 = 0.3 \ A$.$B_{	ext{net}} = |B_1 - B_2| = \left| \frac{\mu_0 N_1 i_1}{2r_1} - \frac{\mu_0 N_2 i_2}{2r_2} ight|$$B_{	ext{net}} = \frac{\mu_0 	imes 10}{2} \left| \frac{0.2}{0.2} - \frac{0.3}{0.4} ight|$$B_{	ext{net}} = 5 \mu_0 \left| 1 - 0.75 ight|$$B_{	ext{net}} = 5 \mu_0 	imes 0.25 = 5 \mu_0 	imes \frac{1}{4} = \frac{5}{4} \mu_0$.

Two concentric coils of $10$ turns each are placed in the same plane. Their radii are $20 \ cm$ and $40 \ cm$ and carry $0.2 \ A$ and $0.3 \ A$ current respectively in opposite directions. The magnetic induction (in $T$) at the centre is

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