Two particles move along two different trajectories in an el

Two particles move along two different trajectories in an electric potential given by V(x,y) k x y, where k is a constant. A contour plot of the potential is shown (lighter color means higher potential, darker means lower potential). Particle A, with charge q 6C takes the straight dashed line. Particle B, also with charge q 6C takes the solid line curved path. The initial position is (x, y) (0.2, 0.2) m. The final position is (x, y) E (0.2, 0.7) m. Which particle gains more electric potential energy? Initial A) Particle A B) Particle B C) Both gain the same amount of potential energy D) Not enough information

Solution

The work done in taking a charge between two points in an electric field generated by fixed charges is independent of the path taken between the points

So the answer is c)