The equipotential lines inside a parallel plate capacitor

Question

a) circles clockwise
b)circles counterclockwise
c)radiates inwards
d)radiates outwards
e)runs parallel to capacitor plates
f)runs perpendicular to capacitor plates

I have narrowed it down to either e) or f) but I think the correct answer would be e) isn't it electric field lines that are perpendicular to equipotenial lines.

Answer 1

Think about a test charge moving from the negative plate to the positive plate.
As it moves from one to the other, the force is parallel to the motion and the work done getting to half way across is the same no matter where on the plate you started. In other words the voltage is the same at all the spots halfway across. And the voltage is the same everywhere on a surface 3/4 of the way across etc. etc. etc. Therefore I claim that the equipotential lines are parallel to the plates.