The work done by the field of a nucleus in a complete circular orbit of the electron is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → Zero
The work done by a force over a small displacement is \( dW = \vec{F}\cdot d\vec{l} \). The force on the electron due to the nucleus is central: it always points along the radius, towards the nucleus. In a circular orbit the displacement is along the tangent, perpendicular to the radius.
\( dW = F\,dl\cos90^\circ = 0 \)
The work is zero for every small step, so it is zero for the complete orbit. The same follows because the electrostatic force is conservative: the electron returns to the point from which it started, so the net work is zero.