Shanika is an engineer at an amusement park who is experimenting with changes to the setup for a magnetic roller coaster ride. In one ride, there are two identical roller coaster cars (orange and green) that start on opposite sides of a large magnet located at the center of a station. Shanika wants to get the largest increase in potential energy she can by moving one car one space to the left or the right. Shanika can move the orange car to point A or point B, or she can move the green car to point C or point D. Which movement should she make? Why will that movement result in the largest increase in potential energy? Describe the magnetic force that will act on the roller coaster car she moves.

Shanika should move the orange coaster car to point B. This movement will result in the largest increase in potential energy. This is because the carts are repelling, which means to increase the potential energy you have to go against the magnetic field. Because the carts are being repelled from the centre magnet to go against the magnetic field you would move the cart closer to the magnet. In this case, moving the orange cart to point b would increase the potential energy greater than any other move.

Explanation:

what i meant in the last sentence was that moving the orange cart to b (closer to centre magnet) would end in a greater potential energy change than moving the other, green, cart closer. This is because of the distances between the carts and the centre magnet. Potential energy does not increase linearly meaning that if a cart is one cart is an inch away from the magnet and another is a foot, if you moved both magnets a cm closer to the centre magnet the one an inch away would have a larger potential energy change.