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A coil of area $2 m^{2}$ and resistance $4 Ω$ is placed perpendicular to a uniform magnetic field of $4 T$ . The loop is rotated by $90 °$ in $0.1$ second. Choose the correct options.

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Average induced emf in the coil is 8V

Average induced current in the circuit is 20A

2 C charge will flow in the coil in above period

Heat produced in the coil in the above period can’t be determined from the given data

answer is B, C, D.

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Detailed Solution

$\begin{array}{rcl} ϕ_{i} & = & B S \cos 0 ° = (4) (2) = 8 W b \\ ϕ_{f} & = & B S \cos 90 ° = 0 \end{array}$

$\begin{array}{rcl} ∆ ϕ & = & 8 W b \\ | e | & = & \frac{∆ ϕ}{∆ t} = \frac{8}{0.1} = 80 V \\ i & = & \frac{| e |}{R} = 20 A \\ ∆ q & = & \frac{∆ ϕ}{R} = 2 C \end{array}$

This current is not constant. So, we cannot find the heat generated unless current function with time is not known.

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