Electric capacitance adding charged particals, rate

[cheff3r]

Okay so the question is

15. (a) Calculate the electric capacitance of the Earth.
(b) Positively charged cosmic ray particles are known to arrive at Earth at the rate of
approximately 1 particle per square centimetre per second. If each particle is
assumed to be singly charged, calculate:-
(i) the electric current carried to the Earth by these particles;
(ii) the rate at which the electrostatic potential of the Earth would rise if there
were no other charge movements to or from the Earth.

my solution
a) knowing Earth's radius of 6380km
C=4*(pi)*ε*R
=4*3.141*8.85*10^-12*6380*10^3
=709.53 mF

b) my problem with b is up until now the queestions not involving flow of charge, so here's my guess its something to do with divergence (we slightly touched on the topic in class) on the other hand doesn't it take more energy everytime charge is added to a capacitor so wouldn't that mean it is dependent on time?

 

[kuruman]

(b.i) Current is measured in Amperes. 1 Ampere = 1 Coulomb/second. How many Coulombs/second total reach the Earth's surface?

(b.ii) You know from part (a) that the potential of the Earth is
$$V = \frac{Q}{4\pi\epsilon_{0}R}$$
where Q s the total charge on the Earth at a given time. Can you find an expression for $$\frac{dV}{dt} ?$$