D

Understanding the Relationship Between Electric Field (E) and Electric Potential (V)
In electrostatics, the relationship between electric field (E) and electric potential (V) is given by the equation:

$$ E = -\frac{dV}{dx} $$

This means that the electric field is related to the spatial rate of change of the electric potential. Now, let’s analyze the options one by one:

Option A: If E = 0, V must be zero.
This is incorrect. If the electric field is zero, the electric potential can still have a non-zero constant value.

Option B: If V = 0, E must be zero.
This is also incorrect. The electric field can be non-zero even if the potential is zero. For example, near charged plates, potential can be zero at some point while an electric field is present.

Option C: If E , V cannot be zero.
This statement is also incorrect. The electric potential can be zero while the electric field is non-zero.

Thus, all of the options A, B, and C are incorrect. The correct answer is:

Option D: None of these.