Two concentric circular coils A and B have radii 25 cm and 15 cm and carry currents 10A and 15A respectively. A has 24 turns and B has 18 turns. The direction of currents are in opposite order. The magnetic induction at the common centre of the coils is

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$80 μ_{0} T$

$120 μ_{0} T$

$420 μ_{0} T$

$480 μ_{0} T$

answer is D.

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Detailed Solution

$\begin{array}{l} B = B_{A} - B_{B} = {(\frac{μ_{0} ni}{2 r})}_{A} - {(\frac{μ_{0} ni}{2 r})}_{B} \\ B = \frac{μ_{0}}{2} [\frac{24 \times 10}{25 \times 10^{- 2}} ~ \frac{18 \times 15}{15 \times 10^{- 2}}]; B = 420 μ_{0} T \end{array}$

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