A) \[\pi \,V/m\]
B) \[2\,V/m\]
C) \[10\,V/m\]
D) \[62\,V/m\]
Correct Answer: B
Solution :
From Faraday?s law of electromagnetic induction, the induced emf is equal to negative rate of change of magnetic flux. That is, \[e=-\frac{\Delta \phi }{\Delta t}\] \[\operatorname{Flux} induced = 2\,B\,\,A\,cos\,\,\phi \] where B is magnetic field, and A is area. Given, \[\theta = 0{}^\circ , \,\Delta t =\frac{1}{100}s\] \[\Delta f= 2 \times 0.01 \times \,\,\pi \,\times {{\left( 1 \right)}^{2}}\times 200 \times cos 0{}^\circ \] \[\therefore \,\,\,\,\,\,\,e\,\,=\,\,\frac{-\,2\times 0.01\times \pi \times {{(1)}^{2}}\times 200}{100}=-\,4\pi \,volt\] Circumference of a circle of radius r is \[2\pi r\]. Induced electric field E is, \[E=\frac{\left| e \right|}{2\pi r}=\frac{4\pi }{2\pi r}=\frac{2}{1}=2\,\,V/m\]
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