A fellow scientist heard that a Van de Graaff generator built 70 years ago could collect 5.0 C of charge on its dome, which had a radius of 1.1 m, and has challenged you to do the same. You plan to use the same dome with the same radius and the belt you plan to use is 200 mm wide and 10.0 m long (5.0 m to go up to the dome, and 5.0 m to come back down). Charging the belt gives it a surface charge density of 65 μC/m2 . Assume that the belt is being charged at a distance of half of the belt length from the center of the dome.
How much force must your motor be able to exert on the belt in order to accomplish your goal?
The Attempt at a Solution
Not sure how to tackle this problem. My thought is that to get a force, you could find the work done by the motor and divide by the distance. The work could be found by the change in electric potential energy to charge the generator. However, I don't feel confident with this approach.
I did calculate the surface area of the entire belt (2 m2) and the using the given surface charge density find the amount of charge over the entire belt (1.3*10-4 C). That would mean that the belt would have to do a complete pass over 38,461 times...
I don't really have a clue on this problem, if anyone could say if I'm on the right track or help me get going, it would rock. Thanks!