The false statement is Option A.
Reasoning:
By definition, on an equipotential surface the potential
V is the same everywhere, so any two points have
ΔV=0The work done in moving a charge
q through a potential difference
ΔV is
W=qΔV=q×0=0 Hence it's incorrect to say the work is "not zero."
The other options are all true:
B: Equipotentials are surfaces of constant
V.
C: In a uniform field, equipotentials are equally spaced parallel planes.
D:
E is always perpendicular to equipotential surfaces.