A particle of specific charge (q/m) is projected from origin of coordinates with initial velocity [u

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4.Moving Charges and Magnetism

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A particle of specific charge $(q/m)$ is projected from the origin of coordinates with initial velocity $[ui - vj]$. Uniform electric magnetic fields exist in the region along the $+y$ direction, of magnitude $E$ and $B.$ The particle will definitely return to the origin once if

A

$[vB /2\pi E]$ is an integer

B

$(u^2 + v^2)^{1/2} [B / \pi E]$ is an integer

C

$[vB / \pi E]$ in an integer

D

$[uB/ \pi E]$ is an integer

Solution

Taking motion along $y$ axis (con by electric field)

$\alpha=y_{0}+u_{y} t+\frac{1}{2} q_{y} t^{2}$

$0=0-v t+\frac{1}{2} \frac{q E}{m} t^{2}$

$t=\frac{2 m v}{q E}$

In this time charge must complex one oe more revolution in $\mathrm{x}$$-$ $\mathrm{z}$ plane due to magnetic field

$T=\frac{2 \pi m}{q B}=-2 \Rightarrow t=n t \ldots(2)$

$\frac{2 m v}{q E}=n \times \frac{2 \pi m}{q B} \Rightarrow \frac{v B}{\pi E}$

Standard 12

Physics

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