Question

A charged particle having charge ${10}^{-6}C$ and mass of ${10}^{-10}kg$ is fired from the middle of the plate making an angle ${30}^o$ with plane of the plate. Length of the plate is 0.17 m and it is sperated by 0.1 m.Electric field $E={10}^{-3}N/C$ is present between the plates.Just outside the plates magnetic field is present. Find the velocity of projection of charged particle and magnitude of the magnetic field perpendicular to the plane of the figure,if it has to graze the plate at C and A parallel to the surface of the plate .(Neglect gravity)

Answer 1

To graze at C:

Using equation of trajectory of parabola
$y=xtan\theta -\frac{a{x}^2}{2v^2{cos}^2\theta }$ ...(i)

Here, $a=\frac{qE}{m}=\frac{{10}^{-6}\times {10}^{-3}}{{10}^{-10}}=10m/s^2$

Substituing in Eq.(i) we have,
$0.05=0.17tan{30}^o-\frac{10\times {\left(0.17\right)}^2}{2v^2\times {\left(\sqrt{3}/2\right)}^2}$

Solving this equation we have,
$v=2m/s$

In magnetic field: $AC=2r$
or $0.1=2r$

or $r=0.05m=\frac{mvcos{30}^o}{Bq}$
$\therefore B=\frac{mvcos{30}^o}{\left(0.05\right)q}$

$=\frac{\left({10}^{-10}\right)\left(2\right)\left(\sqrt{3}/2\right)}{\left(0.05\right)\left({10}^{-6}\right)}=3.46\times {10}^{-3}T$
$=3.46mT$