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(D) The magnetic field at the center of a circular coil of $n$ turns,radius $r$,and current $I$ is given by $B = \frac{\mu_0 n I}{2r}$.Since the two c

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$\frac{10}{3} \mu_0$

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(D) The magnetic field at the center of a circular coil of $n$ turns,radius $r$,and current $I$ is given by $B = \frac{\mu_0 n I}{2r}$.Since the two coils are concentric and carry currents in opposite directions,the net magnetic field at the center is the difference between the individual magnetic fields.Given: $n_1 = n_2 = 20$,$I_1 = 0.4 	ext{ A}$,$r_1 = 30 	ext{ cm} = 0.3 	ext{ m}$,$I_2 = 0.6 	ext{ A}$,$r_2 = 60 	ext{ cm} = 0.6 	ext{ m}$.$B_{	ext{net}} = |B_1 - B_2| = \left| \frac{\mu_0 n_1 I_1}{2 r_1} - \frac{\mu_0 n_2 I_2}{2 r_2} ight|$$B_{	ext{net}} = \frac{\mu_0 	imes 20}{2} \left( \frac{0.4}{0.3} - \frac{0.6}{0.6} ight)$$B_{	ext{net}} = 10 \mu_0 \left( \frac{4}{3} - 1 ight)$$B_{	ext{net}} = 10 \mu_0 \left( \frac{1}{3} ight) = \frac{10}{3} \mu_0 	ext{ T}$.

Two concentric coils of $20$ turns each are placed in the same plane. Their radii are $30 \text{ cm}$ and $60 \text{ cm}$,and they carry $0.4 \text{ A}$ and $0.6 \text{ A}$ currents,respectively,in opposite directions. The magnetic induction at the centre in tesla is ....... .

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