What is the work W done by an external agent moving a test charge q from point A to B in an electrostatic field?

What is the work W done by an external agent moving a test charge q from point A to B in an electrostatic field?

• A. W = q [V(B) − V(A)]
• B. W = 0
• C. W = q [V(A) − V(B)]
• D. W = − q [V(B) − V(A)]

Answer: (A)

The key idea is that the work done by an external agent moving a charge slowly in an electrostatic field equals the increase in the system’s potential energy. The potential energy is U = qV, so the change in potential energy when moving from point A to point B is ΔU = q[V(B) − V(A)]. Therefore, the external work is W_ext = ΔU = q[V(B) − V(A)]. This matches the shown expression. If you were asking about the field’s own work, that would be the negative of this, W_field = −ΔU.

The key idea is that the work done by an external agent moving a charge slowly in an electrostatic field equals the increase in the system’s potential energy. The potential energy is U = qV, so the change in potential energy when moving from point A to point B is ΔU = q[V(B) − V(A)]. Therefore, the external work is W_ext = ΔU = q[V(B) − V(A)]. This matches the shown expression. If you were asking about the field’s own work, that would be the negative of this, W_field = −ΔU.