Earth\'s atmosphere is constantly bombarded by cosmic ray protons that originate

Question

Earth's atmosphere is constantly bombarded by cosmic ray protons that originate somewhere in space. If the protons all passed through the atmosphere, each square meter of Earth's surface would intercept protons at the average rate of 1500 protons per second. What would be the corresponding electric current intercepted by the total surface area of the planet? ANSWER: 122mA. ... I get how to get this but I don't get how to get part B: .... Now imagine we drill a small tunnel that goes straight from the north pole of Earth to the south pole. One of these protons that came from space would go trough the hole and, due to gravity, would get trapped inside the tunnel, and start to go up and down the tunnel, stopping at the north pole only to travel back down to the south pole and so on. Repeating the motion up and down, creating a tiny current inside the tunnel. Find the amount of this current assuming Earth to be homogenous, has a radius of 6360 Km. and a density of 5.5g/cm^3.

Explanation / Answer

We know that 1500 protons crosses 1 m^2 of the Earth's upper atmosphere, so we need to calculate the surface area of the earth. Now, the upper atmospher is many miles up, but it's only thin so I will just use the radius of the earth to calculate the total surface area of the atmospher presented to outer space where cosmic rays come from.

SA = 4 x pi x Re^2
SA = 4 x 3.142 x 6378000m
SA =5.1118 x 10^14 sq m.
With 1500 protons entering per sec then the total number entering the earth' atmospher is:
1500 x 5.1118 x 10^14
7.669 x 10^17
Total charge then = +1.6 x 10^-19 x 7.669 x 10^17
Total charge = 0.1227C

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