A) \[\pi \,volt/m\]
B) \[2\,volt/m\]
C) \[10\,volt/m\]
D) \[62\,volt/m\]
Correct Answer: B
Solution :
In a constant magnetic field conducting ring oscillates with a frequency of 100 Hz. i.e. \[T=\frac{1}{100}s,\]in time \[\frac{T}{2}\] flux links with coil changes from \[BA\] to zero. Þ Induced emf = \[\frac{\text{change in flux}}{\text{time}}\] \[=\frac{BA}{T/2}=\frac{2BA}{T}\]\[=\frac{2B\times \pi {{r}^{2}}}{T}\]\[=\frac{2\times 0.01\times \pi \times {{1}^{2}}}{1/100}=4\pi V\] Induced electric field along the circle, using Maxwell equation \[\oint{E.dl=-\frac{d\varphi }{dt}}\]\[=A\frac{dB}{dt}=e\] Þ \[E=\frac{1}{2\pi r}\times \left( \pi {{r}^{2}}\times \frac{dB}{dt} \right)=\frac{e}{2\pi r}=\frac{4\pi }{2\pi r}=2\,V/m\]
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