Magnetic Effects Of Current Question 359
Question: An electron moves in a circular orbit with a uniform speed v. It produces a magnetic field B at the centre of the circle. The radius of the circle is proportional to [CBSE PMT 2005]
Options:
A) $ \frac{B}{v} $
B) $ \frac{v}{R} $
C) $ \sqrt{\frac{v}{B}} $
D) $ \sqrt{\frac{B}{v}} $
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Answer:
Correct Answer: C
Solution:
Electric current corresponds to the revolution of electron is $ i=\frac{ev}{2\pi r} $ Magnetic field due to circular current at the centre $ B=\frac{{\mu_{0}}}{4\pi }.\frac{2\pi ,i}{r}=\frac{{\mu_{0}}}{4\pi }.\frac{ev}{r^{2}} $
Þ $ r=\sqrt{\frac{{\mu_{0}}}{4\pi }.\frac{ev}{B}} $
Þ $ r\propto \sqrt{\frac{v}{B}} $ .
BETA
