The equipotential lines inside a parallel plate capacitor
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.
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.
You are correct that the electric field lines are perpendicular to the equipotential lines. However, this relationship allows us to determine the orientation of the equipotential lines inside a parallel plate capacitor.
In the case of a parallel plate capacitor, the electric field lines run from the positive plate to the negative plate. These field lines are uniformly distributed and run parallel to the capacitor plates.
Now, let's consider the orientation of the equipotential lines. Equipotential lines are lines that connect points of equal potential. In the case of a parallel plate capacitor, since the electric field lines run parallel to the plates, the electric potential (voltage) between the plates is constant, meaning all points on the plates have the same potential.
As a result, the equipotential lines inside a parallel plate capacitor run parallel to the capacitor plates. Therefore, the correct answer is e) the equipotential lines run parallel to the capacitor plates.