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Q. The work done to move a unit charge along an equipotential surface from $P$ to $Q$

Electrostatic Potential and Capacitance

Solution:

Work done to move a unit charge along an equipotential surface from $P$ to $Q$,
$W= -\int\limits_{P}^{Q} \vec{E} . \overrightarrow{dl}$
On equipotential surface $\vec{E}\, \bot \,d \vec{l} $
$W =- \int\limits_{P}^{Q} E\left(dl\right)cos\,90^{\circ}=0$