Question
Find the condition under which the charged particles moving with different speeds in the presence of electric and magnetic field vectors can be used to select charged particles of a particular speed.
✓
Answer
The velocity $\vec{v}$, of the charged particles, and the $\overrightarrow{E}$ and $\overrightarrow{B}$ vectors, should be mutually perpendicular. Also the forces on q, due to $\overrightarrow{E}$ and $\overrightarrow{B}$ must be oppositely directed. 
$qE=qvB$ $or\text{ }v=\frac{E}{B}$
$qE=qvB$ $or\text{ }v=\frac{E}{B}$ Alternate Answer
Force due to electric field $= q\overrightarrow{E}$ Force due to magnetic field $=q\text{ }(\overrightarrow{v}\times\overrightarrow{B} )$ The required condition is $q\overrightarrow{E}=-q\text{ }(\overrightarrow{v}\times\overrightarrow{B})$ $[or\text{ }\overrightarrow{E}=-(\overrightarrow{v}\times\overrightarrow{B})=(\overrightarrow{B}\times\overrightarrow{v})]$Need a full question paper?
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