The correct answer is A. 100 kV/m.
The electric field strength is given by the equation $E = \frac{V}{d}$, where $V$ is the potential difference and $d$ is the distance between the plates. In this case, $V = 400 V$ and $d = 4 mm = 0.004 m$. Substituting these values into the equation, we get $E = \frac{400 V}{0.004 m} = 100,000 V/m = 100 kV/m$.
Option B is incorrect because it is half the correct value. Option C is incorrect because it is one-fourth the correct value. Option D is incorrect because it is one-tenth the correct value.