7.1.3. A particle with a charge $q$ and a mass $m$ passes through a region of a uniform electric field of length $d$ in time $t$. The velocity $v$ of a particle entering the field is directed along the field. Determine the electric field intensity.
Solution
The motion of particle is accelerated by electric field, so $$d = vt-\frac{at^2}{2} \quad(1)$$ Applying Newton Second Law $$F = qE = ma$$ then, $$a = \frac{qE}{m} \quad(2)$$ Putting $(2)$ into $(1)$$$\boxed{E = 2m\frac{d-vt}{qt^2}}$$