Electro Magnetic Induction And Alternating Currents Question 350
Question: A conducting ring of radius 1 meter is placed in an uniform magnetic field B of 0.01Telsa oscillating with frequency 100Hz with its plane at right angles to B. What will be the induced electric field [AIIMS 2005]
Options:
A) $ \pi ,volt/m $
B) $ 2,volt/m $
C) $ 10,volt/m $
D) $ 62,volt/m $
Show Answer
Answer:
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 ( \pi r^{2}\times \frac{dB}{dt} )=\frac{e}{2\pi r}=\frac{4\pi }{2\pi r}=2,V/m $
