Magnetic Effects Of Current Question 41
Question: In the figure shown there are two semicircles of radii $ r_{1} $ and $ r_{2} $ in which a current i is flowing. The magnetic induction at the centre O will be
Options:
A) $ \frac{{\mu_{0}}i}{r}(r_{1}+r_{2}) $
B) $ \frac{{\mu_{0}}i}{4}(r_{1}-r_{2}) $
C) $ \frac{{\mu_{0}}i}{4}( \frac{r_{1}+r_{2}}{r_{1}r_{2}} ) $
D) $ \frac{{\mu_{0}}i}{4}( \frac{r_{2}-r_{1}}{r_{1}r_{2}} ) $
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Answer:
Correct Answer: C
Solution:
The magnetic induction due to both semicircular parts will be in the same direction perpendicular to the paper inwards.
$ \therefore B=B_{1}+B_{2}=\frac{{\mu_{0}}i}{4r_{1}}+\frac{{\mu_{0}}i}{4r_{2}}=\frac{{\mu_{0}}i}{4}( \frac{r_{1}+r_{2}}{r_{1}r_{2}} )\otimes $
BETA
