# Does current flow in the wire when only one terminal of the battery is earthed?

Let me specify beforehand that this question has been asked previously but I haven't been able to satisfy my curiosity.
I know a battery maintains a potential difference between it's terminals , let's say that the ground is at 0 potential for my question , then with respect to the ground both the terminals are at non-zero potentials.Now if I were to take a wire connect it's ends to ground and to either one of the battery terminals , shouldn't there be a current , at least momentarily?
I think there should be something , there is a potential difference so there should be an electric field pushing on the free electrons in the intervening conductor.

The argument I have read everywhere is that the circuit is not complete so current does not flow but again we have a momentary current across a circuit having a battery and capacitor.What exactly is the explanation , for/against the current flowing in that wire.

I know a battery maintains a potential difference between it's terminals , let's say that the ground is at 0 potential for my question , then with respect to the ground both the terminals are at non-zero potentials.

This statement depends on what you mean by "ground". In electrical power systems "ground" refers to the earth, or "earth ground" because most systems around the world have a conductive connection to earth ground. Unless one of the battery terminals, or a wire connected to one of its terminals, is physically connected to the earth, one would normally consider the potential between either battery terminal and "ground" to be zero. However, capacitance always exists between any conductors, and that would include the battery terminals and ground or any other conductor. The amount of capacitance would, however, be undefined without knowledge of the position of the terminals with respect to other nearby charges, which can vary.

Now if I were to take a wire connect it's ends to ground and to either one of the battery terminals , shouldn't there be a current , at least momentarily?

Yes. Whenever you connect one of the terminals to something conductive (be it earth ground or simply a conductor), there will be electrostatic repulsion or attraction of the charges on the conductive body the battery is connected to, causing a momentary current (movement of charge) to or away from the surface of the conductive body.

The argument I have read everywhere is that the circuit is not complete so current does not flow but again we have a momentary current across a circuit having a battery and capacitor.What exactly is the explanation , for/against the current flowing in that wire.

You are correct. You don't need a complete, as in conductively complete, circuit in order for there to be movement of charge. A capacitor is a perfect example. No current flows through the dielectric between the plates of a capacitor. Yet if it is connected to a battery, the battery delivers charge to one plate, and receives charge from another. It will eventually cease when the voltage across the capacitor equals the battery voltage.

Bottom line, the explanation is whenever there is movement of charge, even if temporarily, we have by definition current.

Hope this helps.

• ok , so current flows and stops instantly , that means no force on free electrons after a while , so can I conclude that the battery terminal and the 'ground' have become equipotential ? , if yes then is it same as that of the connected battery terminal . I asked a question previously about a stretch of wire being connected to one terminal of battery , and people said that a momentary current will flow and then stop after the wire has become equipotential to the battery terminal , what is the scenario here ? Commented May 22, 2019 at 19:23
• @ADITYAPRAKASH I wouldn't say "instantly". It depends, for example, on the surface areas involved, how much charge is on the battery, etc.. But you are right that the force ceases when equilibrium is established (charge stops moving). The same thing happens when you create an electrostatic charge rubbing things together. You can conclude that the terminal of the battery that is connected to "ground" will become equipotential once the charge stops moving (current stops). Hope that answers your follow up question. Commented May 22, 2019 at 19:27
• and that equipotential's value would be ? Commented May 22, 2019 at 19:28
• @ADITYAPRAKASH No problem. Did I answer your side question satisfactorily? Commented May 22, 2019 at 19:29
• yes satisfied , but I've got another confusion , in this question and the one about a simple wire being attached to a battery terminal I referred to in my comment .. the battery must participate in transaction of charges to make the attached conductor equipotential so where do the extra charges come from ? the other terminal ? if yes then isn't it reducing its potential further ? Commented May 22, 2019 at 19:38

Yes, according to me, there will be momentary current. Let's say you arranged the circuit in a way so that electrons are pushed into the Earth. Now there will be a force on electrons displacing them but as soon as the electrons are displaced positive charges develop, as the circuit is not complete and no electrons can come from opposite terminal to fill the empty space. The positive charges create a force on the electrons that were going into the Earth, pulling them back. All this happens so quickly that the next instant, current stops.