What condition yields zero work when moving a charge between two points on an electrostatic field?

What condition yields zero work when moving a charge between two points on an electrostatic field?

• A. The two points lie on the same equipotential surface, so V(B) = V(A); W = 0
• B. The path length is zero
• C. The electric field is zero everywhere along the path
• D. The charge is zero

Answer: (A)

When moving a charge in an electrostatic field, the work done by the field depends only on the potential difference between the endpoints: W = q [V(B) − V(A)]. If the two points lie on the same equipotential surface, their potentials are equal, so V(B) − V(A) = 0 and the field does zero work on the charge regardless of the path taken. This is why staying on an equipotential guarantees no work is required to move the charge. Other scenarios are special cases or not generally applicable: a path of zero length implies no movement at all, so it isn’t a meaningful transfer between two distinct points; a field that is zero along the path is a specific condition not required by the endpoints themselves; and a zero charge would trivially yield zero work but isn’t the general situation being considered.

When moving a charge in an electrostatic field, the work done by the field depends only on the potential difference between the endpoints: W = q [V(B) − V(A)]. If the two points lie on the same equipotential surface, their potentials are equal, so V(B) − V(A) = 0 and the field does zero work on the charge regardless of the path taken. This is why staying on an equipotential guarantees no work is required to move the charge.

Other scenarios are special cases or not generally applicable: a path of zero length implies no movement at all, so it isn’t a meaningful transfer between two distinct points; a field that is zero along the path is a specific condition not required by the endpoints themselves; and a zero charge would trivially yield zero work but isn’t the general situation being considered.