Question

If the potential energy at infinity is taken as zero, then the electrostatic potential energy at a point is:

Options

• The work done in bringing the charge from infinity to that point

• The work done in moving the charge from that point back to infinity

• The total charge of the system divided by the distance moved

• Always equal to the kinetic energy of the charge at that point

Answer 1

Under the standard convention of taking the potential energy at infinity as zero, the potential energy at a point is the work done in bringing the charge from infinity to that point. This follows directly from $\Delta U = U_P - U_R$ with $U_R = 0$ at infinity.