Questions: Electric Potential and the Potential-Field Relationship
2 questions to test your understanding
Score: 0 / 2
Question 1 Short Answer
If the electric potential is constant throughout a region (V = constant), what is the electric field in that region?
Think about your answer, then reveal below.
Model answer: E⃗ = 0. Since E⃗ = −∇V and the gradient of a constant is zero, the electric field is zero everywhere in that region.
This is a direct application of E⃗ = −∇V. The field measures how quickly potential changes with position — if potential does not change, there is no field. This is why the interior of a conductor (which is an equipotential) has zero field.
Question 2 Short Answer
You move a +2 μC charge from point A to point B, where V_A = 100 V and V_B = 40 V. How much work does the electric field do on the charge?
Think about your answer, then reveal below.
Model answer: W = q(V_A − V_B) = (2×10⁻⁶ C)(100 − 40 V) = 1.2×10⁻⁴ J = 0.12 mJ. The field does positive work because the positive charge moves from higher to lower potential.
Work done by the electric field equals W = q ΔV = q(V_initial − V_final). This is analogous to gravity doing positive work when an object falls to lower gravitational potential energy. A positive charge moving to lower potential is like a ball rolling downhill — the field accelerates it, so the field does positive work.