Magnetic Effects Of Current Question 233
Question: In the following figure a wire bent in the form of a regular polygon of n sides is inscribed in a circle of radius $ a $ . Net magnetic field at centre will be
Options:
A) $ \frac{{\mu_{0}}i}{2\pi a}\tan \frac{\pi }{n} $
B) $ \frac{{\mu_{0}}ni}{2\pi a}\tan \frac{\pi }{n} $
C) $ \frac{2}{\pi }\frac{ni}{a}{\mu_{0}}\tan \frac{\pi }{n} $
D) $ \frac{ni}{2a}{\mu_{0}}\tan \frac{\pi }{n} $
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Answer:
Correct Answer: B
Solution:
[b] Magnetic field at the centre due to one side $ B_{1}=\frac{{\mu_{0}}}{4\pi }.\frac{2i\sin \theta }{r} $ Where $ r=a\cos \theta $ So $ B_{1}=\frac{{\mu_{0}}}{4\pi }.\frac{2i\sin \theta }{a\cos \theta }=\frac{{\mu_{0}}i}{2\pi a}\tan \theta $ Hence net magnetic field $ B_{net}=n\times \frac{{\mu_{0}}i}{2\pi a}\tan \frac{\pi }{n} $
BETA
