Question

A point charge q of mass m is placed in front of a uniformly charged infinite sheet and released. The surface charge density of sheet is sigma C m-2. The kinetic energy of charge after t second is [NCERT Pg. 39].

Answer 1

Answer:

Kinetic energy after time t sec is $=\frac{q^2\sigma^2 t^2}{2m\epsilon_0^2}$

Explanation:

Infinite sheet provides constant electric field which is eual to, $E=\frac{\sigma}{\epsilon_0}$

Force acted upon charge q by this electric field, $F=q*E$ , which is also constant.

A constant force provide  constant accleration.

Using $F=m*a$ and equating with force by electric field $F=q*E$

we get,

$\implies m*a= q*E$

$\implies a=\frac{q*E}{m}$

Using newton's equation of motion,

$v=u+at$

where u is the initial velocity,

v is final velocity

and t is the time

Here, u=0,$a=\frac{q*E}{m}$

$\implies v=0+(\frac{q*E}{m}*t )$

$\implies v=(\frac{q}{m}*\frac{\sigma}{\epsilon_0} *t )$

$\implies v=\frac{q\sigma t}{m\epsilon_0}$

velocity after t time is = $\implies v=\frac{q\sigma t}{m\epsilon_0}$

Kinetic enregy = $\frac{1}{2}mv^2 = \frac{1}{2}m*(\frac{q\sigma t}{m\epsilon_0})^2$

Kinetic energy= $=\frac{q^2\sigma^2 t^2}{2m\epsilon_0^2}$

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