Which of the following expresses the relationship between the electric field E and the electric potential V?

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The field is the negative spatial rate of change of the electric potential: E = -∇V. This means the electric field points in the direction in which the potential decreases most rapidly. If you imagine V as a landscape, a positive test charge “rolls” downhill, along the direction of steepest descent, which is why the field points toward lower potential. In electrostatics, where the field has no curl, this gradient relationship holds and the line integral of E between two points equals the negative change in potential: ∫ E·dl = V(initial) - V(final). The other statements don’t capture this connection: curl E = -∂B/∂t is Faraday’s law about changing magnetic fields, not about potential; V = ∇×E would misattribute a curl operator to a scalar potential; and E = ε0 ∇V lacks the necessary minus sign and is not the correct expression.