The potential difference ΔV between two points a and b is defined as:

The potential difference ΔV between two points a and b is defined as:

• A. ΔV = V(b) − V(a) = − ∫_a^b E · dl
• B. ΔV = V(a) − V(b) = ∫_a^b E · dl
• C. ΔV = ∫_a^b E · dl
• D. ΔV = ∫_a^b B · dl

Answer: (A)

Potential difference is tied to how much work per unit charge you do moving between two points, with the sign chosen so that potential drops as you move in the direction of the electric field. This leads to ΔV = V(b) − V(a) = − ∫_a^b E · dl, because the electric field E = −∇V means that the line integral of E along the path from a to b represents the negative change in potential. In other words, the integral of E · dl from a to b gives the negative of the change in potential, so directly integrating E without the minus sign would yield V(a) − V(b) rather than ΔV. The magnetic field cannot define a scalar potential difference in this electrostatic sense, since ∫ B · dl is not how electrostatic potential differences are determined.

Potential difference is tied to how much work per unit charge you do moving between two points, with the sign chosen so that potential drops as you move in the direction of the electric field. This leads to ΔV = V(b) − V(a) = − ∫_a^b E · dl, because the electric field E = −∇V means that the line integral of E along the path from a to b represents the negative change in potential. In other words, the integral of E · dl from a to b gives the negative of the change in potential, so directly integrating E without the minus sign would yield V(a) − V(b) rather than ΔV. The magnetic field cannot define a scalar potential difference in this electrostatic sense, since ∫ B · dl is not how electrostatic potential differences are determined.