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Two concentric circular coils with radii 2cm and 1000 cm and number of turns 20 and 200 respectively are placed co-axially with center’s coinciding .The mutual inductance of this arrangement will be….(approximately)

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$8 \times 10^{- 8} H$

$64 \times 10^{- 8} H$

$32 \times 10^{- 8} H$

$16 \times 10^{- 8} H$

answer is C.

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Detailed Solution

$ϕ_{12} α I$

$ϕ_{12} = M I$

$B N_{2} A = M I$

$\frac{μ_{0} I}{2 r_{2}} . N_{1} N_{2} A = M I [∵ B = \frac{μ_{0} N_{1} I}{2 r_{2}}]$

$\frac{μ_{0}}{2 r_{2}} N_{1} N_{2} π r_{1}^{2} = M$

$\frac{4 π \times 10^{- 7} \times 20 \times 200 \times π \times {(2 \times 10^{- 2})}^{2}}{2 \times 1000 \times 10^{- 2}} = M = 32 \times 10^{- 8} H$

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