Two concentric circular coils A and B have radii 25cm and 15cm 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

r_{A} = 25 cm = 25 \times 10^{- 2} m,

$r_{B} = 15 cm = 15 \times 10^{- 2} m$

$n_{A} = 24, n_{B} = 18 i_{A} = 10 A, i_{B} = 15 A$

$B = B_{A} - B_{B}$

$\begin{matrix} B = \frac{μ_{0} n_{A} i_{A}}{2 r_{A}} - \frac{μ_{0} n_{B} i_{B}}{2 r_{B}} \\ B = \frac{μ_{0} \times 24 \times 10}{2 \times 25 \times 10^{- 2}} - \frac{μ_{0} \times 18 \times 15}{2 \times 15 \times 10^{- 2}} \end{matrix}$

$= μ_{0} (480 - 900)$

$= 420 μ_{0} T$

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