An insulated copper wire of 100 turns is wrapped around a wooden cylindrical core of cross-sectional area . [2023]

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Solution

Q.
An insulated copper wire of 100 turns is wrapped around a wooden cylindrical core of cross-sectional area $24 {cm}^{2}$ . The two ends of the wire are connected to a resistor. The total resistance in the circuit is $12 Ω$ . If an externally applied uniform magnetic field in the core along its axis changes from 1.5 T in one direction to 1.5 T in the opposite direction, the charge flowing through a point in the circuit during the change of magnetic field will be _____ mC. [2023]

Ans.
(60)

$Δ Q = - \frac{Δ ϕ}{R} = - (\frac{ϕ_{2} - ϕ_{1}}{R})$

$ϕ_{1} = N B A$

$ϕ_{2} = - N B A$

$∴$ $Δ Q = \frac{2 N B A}{R} = \frac{2 \times 100 \times 1.5 \times 24 \times 10^{- 4}}{12}$

$= 6 \times 10^{- 2} C = 60 mC$

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