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In the fig. there are two semicircles of radius r_1 \: \: and\: \: r_2 in which a current i is flowing. The magnetic induction at centre O will be

Option: 1

\frac{\mu _{0}I}{r}\left [ r_{1}+r_{2} \right ]


Option: 2

\frac{\mu _{0}I}{4}\left [ r_{1}-r_{2} \right ]


Option: 3

0


Option: 4

\frac{\mu _{0}i}{4}\left [ \frac{r_{2}+r_{1} }{r_1r_2}\right ]


Answers (1)

best_answer

The magnetic field of Semicircular arc -

B= \frac{\mu_{o}}{4\pi} \:\frac{\pi i}{r}= \frac{\mu_{o}i}{4r}

B_{ARC}= \frac{\mu _{0}i}{4r_1}  

So B_{net}= \frac{\mu _{0}i}{4r_1}+\frac{\mu _{0}i}{4r_2}

 

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chirag

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