Define electric potential and describe its relation to the electric field.

Define electric potential and describe its relation to the electric field.

• A. V is the work per unit charge to bring a test charge from infinity to a point; E = ∇V
• B. V is the energy density; E = ∂V/∂t
• C. V is the force per unit charge; E = ∇V
• D. V is the work per unit charge to bring a test charge from infinity to a point; E = −∇V

Answer: (D)

Electric potential represents the work that would be done per unit positive charge to move a test charge from infinity to a point, using a fixed reference where potential is zero at infinity. This makes potential a scalar field that tells you how much energy per charge is available at each point. The electric field is the force per unit charge that a test charge would experience, and it relates to the potential through E = −∇V. The minus sign is crucial: it means the field points in the direction in which the potential decreases most rapidly. In other words, as you move in the direction of the electric field, the potential falls most quickly. The magnitude of E tells you how steeply V changes in space. Putting these together, the work done by the field when moving a unit charge from one point to another is the negative change in potential, W_field = −ΔV. The other statements are not correct because potential is not energy density, E is not simply ∂V/∂t, and potential is not the force per unit charge (that would be the electric field).

Electric potential represents the work that would be done per unit positive charge to move a test charge from infinity to a point, using a fixed reference where potential is zero at infinity. This makes potential a scalar field that tells you how much energy per charge is available at each point.

The electric field is the force per unit charge that a test charge would experience, and it relates to the potential through E = −∇V. The minus sign is crucial: it means the field points in the direction in which the potential decreases most rapidly. In other words, as you move in the direction of the electric field, the potential falls most quickly. The magnitude of E tells you how steeply V changes in space.

Putting these together, the work done by the field when moving a unit charge from one point to another is the negative change in potential, W_field = −ΔV. The other statements are not correct because potential is not energy density, E is not simply ∂V/∂t, and potential is not the force per unit charge (that would be the electric field).