# Work done by an electric field in this case

Assume the following problem:

Two parallel-plate capacitors with different distances between the plates are connected in parallel to a voltage source. A point positive charge is moved from a point 1 that is exactly in the middle between the plates of a capacitor $$C_1$$ to a point 2 (of a capacitor $$C_2$$) that lies at a distance from the negative plate of $$C_2$$ equal to half the distance between the plates of $$C_1$$. Is any work done in the process by the electric field?

My Approach: Since the motion of the charge is perpendicular to the electric field of the capacitors, the work done in such a case would be zero. Hence, no work is done in the process by the electric field

Textbook Approach: The textbook says that the potential at point 1 is lower than the potential at point 2, hence $$W = Q(V_2-V_1) > 0$$ or positive work is done in moving the charge from 1 to 2

Where am I going wrong here? I don't see any mistake in my application of concepts. Is the electric field of a capacitor not always parallel and would I also have to account for edge effects or something similar?