# Can electrostatic induction occur between two equal potentials?

Referring to a situation like shown in this basic diagram of electrostatic induction:

Does electrostatic induction occur if you have charged objects on both sides of a grounded conductive sphere like shown? For the sake of the purpose of this question, lets say the two charged rods have larger cross sectional areas than the sphere and that both of the rods are charged to the same potential so that there's effectively no electric field between the ends of the rods:

Can electrostatic induction occur between the rods and the sphere even if the electric field between the rods is zero? My guess would be no, because the opposing electric charge would eliminate the field lines and thus it would be as if there was no electric potential, at least as long as the sphere was within the area between the two rods:

But I suspect that there's some complication to this I'm not understanding, which is why I'm asking.

• The explanation of your question is quite fuzzy. Please try to make the question more understandable and clear.
– Sam
Jun 25, 2020 at 1:54

The key here is the "ground". According to your picture, you can see immediately that there is an electric field from the two rods acting (in the downward direction) on the wire connecting between the sphere and the ground. This electric field will 'kick' electrons in the wire, and generate current. The sphere will get charged after a while (it loses electrons). After the sphere is charged, it has some electrical potential difference from the ground, and hence generate electric field in the opposite direction (in this case, upward). That way, it can become equilibrium (so electrons in the wire experience no electric field).

So, the sphere will get negatively charged, but uniformly.

Ps. If this sphere is not grounded, nothing happens.

• That makes sense. After considering this question some more, does it make sense to go about thinking of the induced voltage as being from the vertical component of the electric field? In other words, between the axial surfaces of the charged rods the electric field wouldn't have a vertical component but beyond that point you could think of the electric field as having tan(angle with horizontal)*horizontal E-field? Maybe I should put in a graphic for what I'm describing, but something like that.
– Tom
Jun 28, 2020 at 20:41
• Yes, it is definitely correct to think as a voltage from the vertical electric field! Jun 29, 2020 at 7:34

Yes, it will.

You are thinking that with balanced electrostatic forces, there is no force to make electrons move. That's reasonable.

But when electrons can move from an area of high potential to an area of low potential, some of them will randomly do that. And they are less likely to move back to the high potential area than others are to move away.

When there is no way out of the area with uniform potential, they move randomly and the net result is no motion. When there is a way out, more of them escape than return.

Here is an example. Pour an acid solution into a glass vessel. Put a wide-radius copper cylinder into the acid. Connect it to one pole of a 100 volt battery, with the other pole connected to ground. You have created an electric potential, but you are not putting any force on charges in the acid. An equal number of positive hydrogen ions and negative other ions move randomly through the acid.

Put a thin copper cylinder in the center of the big cylinder. Nothing happens. The potential does nothing.

Connect the other end of your battery to the center cylinder. Now you will get a current. Charges in the acid will move, positive charges toward the cathode and negative charges toward the anode. Copper atoms will be dissolved at the anode and deposited on the cathode. Hydrogen ions from water may lose their charge at one electrode and turn in to hydrogen gas, while oxygen atoms do the same at the other electrode.

It's because they have a place to go.

Static electricity provides only a potential, until it gets a chance to move.

• Interesting, that kind of makes me think of the Aharonov Bohm effect, where the magnetic potential itself can affect electrons despite there not being a magnetic field. But I guess this can be reasoned with just classical physics.
– Tom
Jun 28, 2020 at 20:06
• A very interesting answer by the way. The answer above seems more direct for this sort of question so I think I'm going to have the points go to that one, but I appreciate it.
– Tom
Jun 30, 2020 at 19:53