Magnetic Effects Of Current Question 429
Question: A current I flows through a thin wire shaped as regular polygon of n sides which can be inscribed in a circle of radius R. The magnetic field induction at the center of polygon due to one side of the polygon is
Options:
A) $ \frac{{\mu_{0}}I}{\pi R}( \tan \frac{\pi }{n} ) $
B) $ \frac{{\mu_{0}}I}{4\pi R}( \tan \frac{\pi }{n} ) $
C) $ \frac{{\mu_{0}}I}{2\pi R}( \tan \frac{\pi }{n} ) $
D) $ \frac{{\mu_{0}}I}{2\pi R}( \cos \frac{\pi }{n} ) $
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Answer:
Correct Answer: C
Solution:
[c] $ B=\frac{{\mu_{0}}I}{4\pi r}[ 2,\sin \frac{\pi }{n} ] $ $ \cos \frac{\pi }{n}=\frac{r}{R} $ But or $ r=R\cos \frac{\pi }{n} $
$ \therefore ,B=\frac{{\mu_{0}}I}{4\pi ,R,\cos \frac{\pi }{n}}[ 2,\sin \frac{\pi }{n} ]=\frac{{\mu_{0}}I}{2\pi R}[ \tan ,\frac{\pi }{n} ] $
BETA
