A small conducting sphere S is suspended from a very long light insulating thread between two metal plates X and Y. The plates are connected to a voltage source and a sensitive current measuring device A. After being given an initial displacement from its vertical position OP, the sphere moves to one of the plates, touches it, moves rapidly to the other, touches that, and this motion repeats itself. The device A registers a current. P (a) Explain what is happening. (b) Deduce expressions for (c) (i) (ii) the charge on the sphere in terms of its radius R and the battery p.d. V when in contact with X (assuming that the sphere acts as if "isolated"), the electrostatic force on the sphere in terms of R, V and the distance x between the metal plates (assuming that the field is uniform), (iii) the acceleration of the sphere in terms of R, V, x and m, the mass of the sphere (assuming that gravity plays no part), (iv) the time for the sphere to go from X to Y (assuming that x is much greater than R and that the impacts are totally inelastic). Hence show that the frequency of the oscillation might be expected to be proportional to Vlx and to (R/m) 1/2.