Magnetic Effects Of Current Question 432
Question: Two similar coils of radius R are lying concentrically with their planes at right angles to each other. The currents flowing in them are I and 2I, respectively The resultant magnetic field induction at the centre will be:
Options:
A) $ \frac{\sqrt{5}{\mu_{0}}I}{2R} $
B) $ \frac{3{\mu_{0}}I}{2R} $
C) $ \frac{{\mu_{0}}I}{2R} $
D) $ \frac{{\mu_{0}}I}{R} $
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Answer:
Correct Answer: A
Solution:
[a] The magnetic field, due the coil, carrying current $ I $ Ampere $ B_{1}=\frac{{\mu_{0}}I}{2R} $ The magnetic field due to the coil, carrying current I Ampere $ B_{2}=\frac{{\mu_{0}}(2I)}{2R} $ The resultant B $ B_{net}=\sqrt{B_{1}^{2}+B_{2}^{2}+2B_{1}B_{2},\cos ,\theta ,}\theta =90^{o} $ $ B_{net}=\sqrt{B_{1}^{2}+B_{2}^{2}}=\frac{{\mu_{0}}(2I)}{2R}\sqrt{1+4}=\frac{\sqrt{5}{\mu_{0}}I}{2R} $
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