Question 790: Electrostats & Capacitance

Question

A charged particle of mass ' $m$ ' and charge ' $q$ ' is at rest. It is acce:lerated in a uniform electric field of intensity ' $E$ ' : for time ' $t$ '. The kinetic energy of the particles after time $t$ is

Accepted Answer

Given:
Mass of particle $= m$
Charge $= q$
Electric field intensity $= E$
Time for which itÃ¢ÂÂs accelerated $= t$
Initial velocity $= 0$ (at rest)
Step 1: Find the force acting on the particle
The force $F$ on a charged particle in an electric field:
$$ F = qE $$
Step 2: Find the acceleration
By NewtonÃ¢ÂÂs second law,
$$ F = ma \ \Rightarrow a = \frac{F}{m} = \frac{qE}{m} $$
Step 3: Find the velocity after time $t$
Since initial velocity $u = 0$,
$$ v = u + at = 0 + \left(\frac{qE}{m}ight)t = \frac{qEt}{m} $$
Step 4: Find the kinetic energy
Kinetic energy,
$$ K.E. = \frac{1}{2} m v^2 $$
Substitute the value of $v$:
$ K.E. = \frac{1}{2} m \left(\frac{qEt}{m}ight)^2 = \frac{1}{2} m \cdot \frac{q^2 E^2 t^2}{m^2} $
$ = \frac{1}{2} \cdot \frac{q^2 E^2 t^2}{m} $
Final Answer:
$$ \boxed{\frac{E^2 q^2 t^2}{2 m}} $$
So, the correct option is
Option B
.

Answer

$\frac{E q m}{2 t}$

Answer

$\frac{E^2 q^2 t^2}{2 m}$

Answer

$\frac{2 \mathrm{E}^2 \mathrm{t}^2}{\mathrm{mq}^2}$

Answer

$\frac{\mathrm{Eqt}}{\mathrm{m}}$

Electrostats & Capacitance

A charged particle of mass ' m ' and charge ' q ' is at rest. It is acce:lerated in a uniform electric field of intensity ' E ' : for time ' t '. The kinetic energy of the particles after time t is

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