Question

A particle of mass m and charge q is thrown at a speed u against a uniform electric field E. How much distance will it travel before coming to momentary rest?

Answer 1

Given:
Charge of the particle = q
Velocity of projection = u
Electric field intensity = E
Mass of the particle = m
We know that the force experience by a charged particle in an electric field is qE.
Acceleration produced, a = $\frac{qE}{m}$ (Negative because the particle is thrown against the electric field)
Let the distance covered by the particle be s.
Then v² = u² + 2as
[Here, a = deceleration, v = final velocity]
Here, 0 = u² − 2as
$$\begin{gathered} \Rightarrow s=\frac{u^2}{2a} \\ \Rightarrow s=\frac{m{u}^2}{2qE} \end{gathered}$$