The electric field strength near the surface of Earth is about 300 V/m. a) Estim
ID: 2290093 • Letter: T
Question
The electric field strength near the surface of Earth is about 300 V/m.
a) Estimate the magnitude of the charge density on the surface of the Earth. As approximation you can treat the surface of Earth like a flat conducting sheet. Use Gausss Law to calculate the surface charge density. Hint: imagine a Gaussian surface for which it would be easy to calculate the electric flux.
b) Estimate the total charge on Earth
c) What is the value of the electric potential at the Earths surface? Assume the potential is zero at infinity. Treat Earth as a charged sphere.
d) If all the Earths electrostatic potential energy could be harnessed and converted to electric energy, how long could it be used to run the consumer households in the US? The average American household consumes about 500 kWh of energy per month. Assume Earth is one plate of a large capacitor. Clouds above the surface could serve as the second plate. How much energy is stored in this capacitor?
Explanation / Answer
Find the electric force from
Force = field strength x charge on electron = 150 x e
Gravitational force = mg = electron mass x 9.81
Now find the ratio of the two answers.
weight of penny = 0.005 x 9.81
Electric force = 150 x q
So q = (0.005 x 9.81)/150
Note you are in practice unlikely to be able to balance the forces since the charge is in discrete 'lumps' and not continuous...