A) \[\frac{B}{v}\]
B) \[\frac{v}{R}\]
C) \[\sqrt{\frac{v}{B}}\]
D) \[\sqrt{\frac{B}{v}}\]
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 \[r\propto \sqrt{\frac{v}{B}}\].
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