# Discharging by grounding

1. Aug 30, 2011

### fisico30

discharging by grounding....

Hello Forum,

Earth can be considered as a huge conducting sphere with total negative charge Q= -400000 C. The surface charge density is 2.655*10^-9 C/m^2. The electric field is 300 V/m pointing inward. I learned that planet earth can even lose 1500 C per second and gain negative charge of 20 C from lighting bolts.

Let's take a metal sphere of radius r=1m having a negative charge q = - 3C.
We then connect this small sphere to planet earth using a metallic wire. We know that the small sphere will quickly discharge and become neutral.This happens because the small sphere and earth ( the super large sphere) want to reach the same surface potential. Current (charge flow) stops when the potentials are the same. The potential on the surface of a generic sphere of radius r is V = k q/r.

Before connecting them

V_sphere=k q/r = -2.7 x 10^10 (very large)

V_earth= k Q/R = - 5.66 x 10^8 (large too)

where q=-3C and Q= - 400000 C, r=1 and R=6378100 m. After connection the potentials on the two sphere must be the same and charge will move around to make that happen:

q_new/r = Q_new/R

r and R are constants. Why would q_new have to go to zero? Why would the net charge leave the small sphere? Why would more negative charge from the earth not move on the small sphere? What simple thing am I missing?

Usually charge should move onto small objects, protrusions, sharp points...

thanks and sorry if it is a trivial electrostatic question....
Fisico30