Question: Q. 6. Write the condition under which an electron will move undeflected in the presence of crossed electric and magnetic fields.
R [O.D. Comptt. I, II, III 2014]
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Solution:
Ans. $\quad v=\frac{E}{B}$ where $v$ is speed of electron.
Alternatively,
$\left|\vec{F}{E}\right|=\left|\overrightarrow{F{B}}\right|$
[CBSE Marking Scheme 2014]
Detailed Answer :
Crossed electric and magnetic fields are that when electric and magnetic fields are perpendicular to each other, so under such circumstances, electron will move undeflected since electric force gets balanced by magnetic force acting on it.
Hence, $\quad q E=q v B$
where, $q=$ charge, $E=$ electric field, $B=$ magnetic field, $v=$ velocity of the electron
As $q=e$ shows charge on electron, so $e E=e v B$, then $v=\frac{E}{B}$
