Problem A.B,C ( answer all the parts )

The idea of a railgun system can be simply understood with the diagram shown in the figure. First, S1 is closed and S2 is open, the capacitor with capacitance C will be charged by the emf which can supply a voltage up to V. Then, open S1 and close S2, the capacitor will discharge through the rails (two yellow bars) with the projectile (the gray block in between two yellow bars). The projectile has a width w0. The current I(t) flowing through the rail will generate a magnetic field point into the paper plane in between the rails, which will exert a force towarding the right, driving the projectile to move. Assume the projectile is at a distance l0 when the discharge starts, and the effective resistance of the discharging circuit is R (ignore the resistance of the rail and the projectile, and the contacting resistance between the projectile and the rail). Use the vacuum permeability μ0 for this problem.