A fellow scientist heard that a Van de Graaff generator built 70 years ago could collect \(5.0 \mathrm{C}\) of charge on its dome, which had a radius of \(1.1 \mathrm{~m}\), and has challenged you to do the same. The belt you plan to use is \(100 \mathrm{~mm}\) wide and \(10.0 \mathrm{~m}\) long \((5.0 \mathrm{~m}\) to go up to the dome, and \(5.0 \mathrm{~m}\) to come back down). Charging the belt gives it a surface charge density of \(45 \mu \mathrm{C} / \mathrm{m}^{2}\). How much force must your motor be able to exert on the belt in order to accomplish your goal? If you had more freedom in the design, what changes would you make to make the charging process easier on your motor, and why? Would your changes alter only the force required for your motor, or would they also affect the energy required for charging? State any assumptions you make, and state whether or not they are physically reasonable.