Electro Magnetic Induction And Alternating Currents Question 318
Question: A uniform but time-varying magnetic field B(t) exists in a circular region of radius a and is directed into the plane of the paper, as shown. The magnitude of the induced electric field at point P at a distance r from the centre of the circular region [IIT-JEE (Screening) 2000]
Options:
A) Is zero
B) Decreases as $ \frac{1}{r} $
C) Increases as r
D) Decreases as $ \frac{1}{r^{2}} $
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Answer:
Correct Answer: B
Solution:
Construct a concentric circle of radius r.
The induced electric field (E) at any point on the circle is equal to that at P.
For this circle $ \oint{\vec{E}.d\vec{l}=| \frac{d\varphi }{dt} |=A\ | \frac{dB}{dt} |} $ or $ E\times (2\pi r)=\pi a^{2}.| \frac{dB}{dt} | $
$ \Rightarrow E=\frac{a^{2}}{2r}| \frac{dB}{dt} |\Rightarrow E\propto \frac{1}{r} $
