Magnetic Effects Of Current Question 150
Question: A thin circular wire carrying a current I has a magnetic moment M. The shape of the wire is changed to a square and it carries the same current. It will have a magnetic moment [MP PET 2003; MP PMT 2004]
Options:
A) M
B) $ \frac{4}{{{\pi }^{2}}}M $
C) $ \frac{4}{\pi }M $
D) $ \frac{\pi }{4}M $
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Answer:
Correct Answer: D
Solution:
Initially for circular coil $ L=2\pi r $ and $ M=i\times \pi r^{2} $ $ =i\times \pi {{( \frac{L}{2\pi } )}^{2}}=\frac{iL^{2}}{4\pi } $ ….. (i) Finally for square coil $ {M}’=i\times {{( \frac{L}{4} )}^{2}}=\frac{iL^{2}}{16} $ ….. (ii) Solving equation (i) and (ii) $ {M}’=\frac{\pi M}{4} $
BETA
