First slide

Faraday's law of Electromagnetic induction

Question

A circular ring of diameter 20 cm has a resistance 0.01 ohm. How much charge will flow through the ring if it is rotated from position perpendicular to the uniform magnetic field of B = 2T to a position parallel to field

Moderate

A

4 C
B

6.28 C
C

3.14 C
D

25.12 C

Solution

We know that
$\begin{array}{l} e = - \frac{{dΦ}_{m}}{dt} and e = Ri = R (\frac{dQ}{dt}) \\ ∴ R (\frac{dQ}{dt}) = - \frac{{dΦ}_{m}}{dt} or R | dQ | = |{dΦ}_{m}| \\ or | dQ | = \frac{Φ_{mf} - Φ_{mi}}{R} \\ Here Φ_{mf} = \frac{{πd}^{2} B}{4} and Φ_{mi} = 0 \\ ∴ | dQ | = \frac{{πd}^{2} B}{4 R} = \frac{3 \cdot 14 \times (0 \cdot 2)^{2} \times 2}{4 \times 0 \cdot 01} = 6 \cdot 28 C \end{array}$

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