A particle of mass m and charge q is released from rest in a uniform electric field. If there is no other force on the particle, the dependence of its speed v on the distance x travelled by it is corr

Question

A particle of mass m and charge q is released from rest in a uniform electric field. If there is no other force on the particle, the dependence of its speed v on the distance x travelled by it is correctly given by (graphs are schematic and not drawn to scale)

TestHub · Accepted Answer

The particle is at rest initially.

So, the initial velocity $u = 0 m s^{- 1}$ .

The force on the charged particle in the uniform electric field,

$F = q E$

$\Rightarrow m a = q E$

$\Rightarrow a = \frac{q E}{m}$

Applying the velocity-displacement equation under constant acceleration,

$v^{2} = u^{2} + 2 a x$

$\Rightarrow v^{2} = 0^{2} + 2 (\frac{q E}{m}) x$

$\Rightarrow v^{2} = \frac{2 q E}{m} x$

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