Q146 / 170 · Manipal (MET) 2017 · Physics

A charged particle of mass $m$ and charge $q$ is released from rest in a electric field of magnitude $E$. The kinetic energy of the particle after $t$ second is

A
$\frac{q E t}{2 m}$
B
$\frac{q^2 E^2 t}{2 m}$
C
$\frac{q^2 E^2 t^2}{m}$
Correct answer
D
$\frac{q^2 E^2 t^2}{2 m}$

Solution

Force on a particle with charge $q$ in electric field $E$ is $\begin{aligned} F & =q E=m a \\ \therefore a & =\frac{q E}{m}\end{aligned}$ here $a=\frac{v}{t}$ $\therefore \frac{v}{t}=\frac{q E}{m} \Rightarrow v=\frac{q E t}{m}$ Also, kinetic energy is due to velocity $(v)$ is $K=\frac{1}{2} m v^2=\frac{1}{2} m\left(\frac{q E t}{m}\right)^2=\frac{q^2 E^2 t^2}{2 m}$

Hence, the correct answer is option: 'D'.

Relevant Questions

If an electron has an initial velocity in a direction different from that of an electric field, the path of the electron is :2021Electric Field and Electric Field Lines
What is the direction of the electric field at the centre of the square in the figure shown below? Given that, and the side of the square is2020Electric Field and Electric Field Lines
A charged particle of mass 0.003 g is held stationary in space by placing it in a downward direction of electric field of . Then the magnitu2019Electric Field and Electric Field Lines
Three infinitely charged sheets are kept parallel to plane having charge densities as shown. Then, the value of electric field at ' ' is2014Electric Field and Electric Field Lines
How does, the electric field between the plates of a charged cylindrical capacitor vary with the distance from the axis of the cylinder?2012Electric Field and Electric Field Lines
In Millikan's oil drop experiment, a charged drop of mass is stationary between its plates. The distance between its plates is 0.9 cm and po2011Electric Field and Electric Field Lines