Why Does a Negatively Charged Sphere Discharge When Connected to Earth?

[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

 

[eljose79]

Hello Fisico30,

I can explain the process of discharging by grounding in more detail. When a small negatively charged object, like the metal sphere in your example, is connected to a larger conducting object, like the Earth, the negative charge from the small sphere will flow to the larger object until they reach the same potential. This is because in nature, objects tend to move from high potential to low potential in order to achieve equilibrium.

In your example, the potential on the surface of the small sphere is much higher than the potential on the surface of the Earth. This means that the negative charge on the small sphere will flow to the Earth until the potentials are equal. This process will continue until the small sphere becomes neutral and the Earth gains a small negative charge.

You are correct that charge tends to accumulate on sharp points or protrusions, but in this case, the Earth is a much larger and more conductive object, so the charge will flow to it instead of accumulating on the small sphere. This is because the Earth has a much larger surface area and can hold a larger amount of charge.

I hope this helps to clarify the process of discharging by grounding. If you have any further questions, please don't hesitate to ask. Science is all about asking questions and seeking answers!