Two concentric circular coils with radii 1 cm and 1000 cm, and number of turns 10 and 200 respectively, are placed coaxially with centers coinciding. The mutual inductance of this arrangement will be _________ . (Take, ) [2023]

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Solution

Q.
Two concentric circular coils with radii 1 cm and 1000 cm, and number of turns 10 and 200 respectively, are placed coaxially with centers coinciding. The mutual inductance of this arrangement will be _________ $\times 10^{- 8} H$ . (Take, $π^{2} = 10$ ) [2023]

Ans.
(4)

$r_{1} = 1 cm, N_{1} = 10$

$r_{2} = 1000 cm, N_{2} = 200$

$ϕ_{1, 2} = M I_{2}$

$N_{2} {\vec{B}}_{2} \cdot N_{1} {\vec{A}}_{1} = M I_{2}$

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

$\Rightarrow M = \frac{10 \times 200 \times 4 π \times 10^{- 7} \times π \times {(0.01)}^{2}}{2 \times 10}$

$\Rightarrow M = 4 \times 10^{- 8}$

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