A particle of mass ' M ' and charge ' q ' initially at rest is...

Work done by the uniform electric field on the particle is given by $W = qED$.

By the work-energy theorem, the kinetic energy gained by the particle is $K = qED$.

When the particle approaches the fixed static charge $Q$, its kinetic energy is converted into electrostatic potential energy.

At the distance of closest approach $r$, the velocity of the particle becomes zero and the entire kinetic energy is stored as potential energy.

The electrostatic potential energy at distance $r$ is $U = \dfrac{1}{4\pi\epsilon_0} \dfrac{qQ}{r}$.

Equating the kinetic energy and potential energy:

$qED = \dfrac{1}{4\pi\epsilon_0} \dfrac{qQ}{r}$

$r = \dfrac{Q}{4\pi\epsilon_0 ED}$

Answer: $Q/4\pi\epsilon_0 ED$