Electro Magnetic Induction And Alternating Currents Question 456
Question: A conducting circular loop is placed in a uniform magnetic field of 0.04 T with its plane perpendicular to the magnetic field. The radius of the loop starts shrinking at 2 mm/s. The induced emf in the loop when the radius is 2 cm is
Options:
A) $ 4.8\pi \mu ,V $
B) $ 0.8\pi \mu ,V $
C) $ 1.6\pi \mu ,V $
D) $ 3.2\pi \mu ,V $
Show Answer
Answer:
Correct Answer: D
Solution:
-
Induced emf in the loop is given by
$ e=-B.\frac{dA}{dt} $ where A is the area of the loop.
$ e=-B.\frac{d}{dt}(\pi r^{2})=-B,\pi 2r\frac{dr}{dt} $
$ r=2cm=2\times {{10}^{-2}}m $
$ dr=2mm=2\times {{10}^{-3}}m $ ,
$ dt=1s $
$ e=-,0.04\times 3.14\times 2\times 2\times {{10}^{-2}}\times \frac{2\times {{10}^{-3}}}{1}V $
$ =0.32\pi \times {{10}^{-5}}V=3.2\pi \times {{10}^{-6}}V=3.2\pi \mu V $
