A) \[\frac{B}{v}\]
B) \[\frac{v}{B}\]
C) \[\sqrt{\frac{v}{B}}\]
D) \[\sqrt{\frac{B}{v}}\]
Correct Answer: C
Solution :
The time period of electron moving in a circular orbit \[T=\frac{circumference\,of\,circular\,path}{speed}\] \[=\frac{2\pi r}{v}\] and equivalent current due to electron flow \[I=\frac{e}{T}=\frac{e}{(2\pi r/v)}=\frac{ev}{2\pi r}\] Magnetic field at centre of circle \[B=\frac{{{\mu }_{0}}I}{2r}=\frac{{{\mu }_{0}}ev}{4\pi {{r}^{2}}}\] \[\Rightarrow r\,\propto \,\,\sqrt{\frac{v}{B}}\]You need to login to perform this action.
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