faraday's law

Question

A coil of resistance 10Ω and 100 turns has a diameter of 20cm. It is placed with its plane perpendicular to a magnetic field of 3T. If the field is removed in 0.5s, the induced charge is:

RankGuru · Accepted Answer

1. **Induced Charge Formula**: The charge induced in a circuit due to change in magnetic flux is $q = \frac{N\Delta\Phi}{R}$.
2. **Change in Flux ($\Delta\Phi$)**: $\Phi_{initial} = BA$ and $\Phi_{final} = 0$. Area $A = \pi r^2 = \pi (0.1)^2 = 0.0314	ext{ m}^2$.
   $$\Delta\Phi = 3 	imes 0.0314 = 0.0942	ext{ Wb}$$
3. **Calculation**: $q = \frac{100 	imes 0.0942}{10} = 0.942	ext{ C}$.
4. **Conclusion**: The total charge induced is 0.942 C.

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