MCQ
An electron is projected with velocity $\vec v$ in a uniform magnetic field $\vec B$ . The angle $\theta$  between $\vec v$ and $\vec B$  lines between $0^o$ and $\frac{\pi}{2}$ . It velocity $\vec v$ vector returns to its initial  value in time interval of 
  • $\frac{2 \, \pi m}{eB}$
  • B
    $\frac{ \pi m}{eB}$
  • C
    $\frac{ \pi m}{2\,eB}$
  • D
    Depends upon angle between $\vec v$ and $\vec B$

Answer

Correct option: A.
$\frac{2 \, \pi m}{eB}$
a
The electron will move in a circular path The velocity vector returns to its initial value in a time period.

$\mathrm{T}=\frac{2 \pi \mathrm{m}}{\mathrm{qB}}=\frac{2 \pi \mathrm{m}}{\mathrm{eB}}$

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