A) \[\frac{B}{v}\]
B) \[\frac{v}{B}\]
C) \[\sqrt{\frac{v}{B}}\]
D) \[\sqrt{\frac{B}{v}}\]
Correct Answer: C
Solution :
[c] The time period of electron moving in a circular orbit \[T=\frac{\text{circumference}\,\text{of}\,\text{circular}\,\text{path}}{\text{speed}}\] \[=\frac{2\pi r}{v}\] 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 \[B=\frac{{{\mu }_{0}}I}{2r}=\frac{{{\mu }_{0}}ev}{4\pi {{r}^{2}}}\] \[\Rightarrow \] \[r\,\propto \,\,\sqrt{\frac{v}{B}}\]
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