A long solenoid of radius $2 cm$ has $100 turns/cm$ and is surrounded by a $100$ turn coil of radius $4 cm$ having a total resistance $20 Ω$ . If current changes from $5 A$ to $- 5 A$ , find the charge through galvanometer.

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$600 μ C$

$800 μ c$

Zero

$400 μ C$

answer is B.

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Detailed Solution

$ϕ = B π r^{2}$

$ϵ = \frac{d ϕ}{d t} = N π r^{2} \frac{d B}{d t}$

$= N π r^{2} μ_{0} n \frac{d i}{d t}$

$I = \frac{ϵ}{R}$ and $∆ Q = I ∆ t = \frac{N π r^{2} μ_{0} n}{R} ∆ t$

$∆ Q = \frac{100 \times π \times (2 \times 10^{- 2})^{2} \times 10^{4} \times 4 π \times 10^{- 7} \times 10}{20}$

$= 8 \times 10^{- 4} c = 800 μ C$

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