# Does the electrostatic force create current in the circuit?

• erocored
Ohm's law is a transport property, not a potential. Ohm's law is the response of a medium to a generalized force. In this case it's the response of the conduction charges (in a usual metal conduction electrons) to an external electromagnetic field leading to the linear-response equation$\vec{j}=\sigma (\vec{E}+\vec{v} \times \vec{B}).$More generally, of course ##\sigma## depends on the frequency in the Fourier decomposition of the fields or even on the frequency and wave number....

#### erocored

As I understand potential difference is the reason of current. Does it mean that the electrostatic force creates current?

In a conductor yes.

• etotheipi, vanhees71 and erocored
erocored said:
As I understand potential difference is the reason of current. Does it mean that the electrostatic force creates current?
As @kuruman said, in an ordinary conductor, yes. However, that is a very large limitation. Many materials are not conductors and you can very easily have currents without potential differences and potential differences without currents in other materials. So you should not think of that as a general rule, just as a description of the behavior of conductors.

Also, if you have a current source then, even in a conductor you could consider the current to be creating the potential difference instead of the other way around. A conductor merely establishes a relationship between current and potential difference, it does not imply causality.

• erocored
Dale said:
Also, if you have a current source then, even in a conductor you could consider the current to be creating the potential difference instead of the other way around. A conductor merely establishes a relationship between current and potential difference, it does not imply causality.
If a conducting wire is left alone, there is no current. If a potential difference is established across its ends with a battery, there is a current. Arguably, the electrostatic potential difference and hence the electric force derived from it cause the charge carriers to flow from one end to the other. With that understanding, I think it is safe to say that the electrostatic force "creates" the current. That's what I thought OP's initial query was about.

It is circular. Take a length of wire with resistance R. Then the voltage difference between the two ends is related to current by E=IR. You can say that voltage causes the current or that the current causes the voltage. That is why the phrase circular relationship applies.

But there is no current flow or voltage drop unless the wire is part of a closed circuit.

• erocored
kuruman said:
If a conducting wire is left alone, there is no current. If a potential difference is established across its ends with a battery, there is a current.
If a conducting wire is left alone, there is no voltage. If a current is established through the wire with a transistor, there is a voltage.

kuruman said:
Arguably, the electrostatic potential difference and hence the electric force derived from it cause the charge carriers to flow from one end to the other.
Arguably the charge carriers flowing from one end to the other and the electric force derived from it cause the electrostatic potential difference.

kuruman said:
With that understanding, I think it is safe to say that the electrostatic force "creates" the current.
With that understanding, I think it is not safe to say in general that either creates the other.

It depends on the nature of the source. People tend to think in terms of voltage causing current because their most familiar sources are voltage sources (batteries and household power). But current sources do exist and are equally valid sources.

• kuruman
Dale said:
People tend to think in terms of voltage causing current because their most familiar sources are voltage sources (batteries and household power). But current sources do exist and are equally valid sources.
Yes, of course. I didn't think of current sources even though I have used them. Count me as one of these people.

• Dale
anorlunda said:
But there is no current flow or voltage drop unless the wire is part of a closed circuit.
It depends what you mean by a 'circuit'. Charges can build up on a part of a conducting objet when charged particles arrive from elsewhere and they will flow through the conductor until the potential is a minimum all over the object. Likewise a changing magnetic field can cause an emf on a conductor and charges can migrate to one end. So those basic rules that are taught about electricity are not universal. No problem but it should be borne in mind.

Dale said:
Also, if you have a current source then, even in a conductor you could consider the current to be creating the potential difference instead of the other way around. A conductor merely establishes a relationship between current and potential difference, it does not imply causality.
As some recent discussions in this forum show, that's confusing many students. You don't need necessarily a potential which would indeed restrict Ohm's law to DC situations. Ohm's Law is a transport property, i.e., it's the response of a medium to a generalized force. In this case it's the response of the conduction charges (in a usual metal conduction electrons) to an external electromagnetic field leading to the linear-response equation
$$\vec{j}=\sigma (\vec{E}+\vec{v} \times \vec{B}).$$
More generally, of course ##\sigma## depends on the frequency in the Fourier decomposition of the fields or even on the frequency and wave number. If the medium is anisitropic it's a tensor.

For more details, see Landau&Lifhitz, vol. 8.

• etotheipi
erocored said:
As I understand potential difference is the reason of current. Does it mean that the electrostatic force creates current?
No.
Current is created by an emf, not by potential difference.
Electrostatic charge (and voltage) is generated by emf, not the other way, around.

In a battery-resistor circuit, for example, the battery produces an emf which drives charge around the circuit.
The voltage drop across the resistor is just that, a drop not a rise. There is no emf across the resistor.

Prof. R. Shankar gives a good analogy with a ski lift: the lift force is the emf, the battery's electrostatic field is gravity opposing the emf. Then at the top of the lift (the + end of the battery) he has acquired potential at which point he skis down the slope with friction until he arrives at the bottom with zero kinetic energy (zero potential), the friction having dissipated the energy produced by the emf. The power dissipated by the resistor is represented by the friction energy loss.

• erocored
vanhees71 said:
As some recent discussions in this forum show, that's confusing many students.
I think you are missing my main point. I guess I wasn't expressing myself clearly.

The problem that I was addressing above is that ##a=b## does not establish a causal relationship at all. Unfortunately, many students look at an equation like that and think that it means ##a## causes ##b##, which is problematic because it leads to incorrect physical reasoning in some circumstances. Not the least of which is that the equation can also be written ##b=a##.

Equality is not causality. That is, in my opinion, the more important point and the point I was trying to express above.

Although not discussed above, causes preceed effects by definition. So a causal relationship must be of the form ##a(t)=b(t_r)## where ##t_r<t## and in the case of EM ##t_r## is known as the retarded time.

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• sophiecentaur, etotheipi, anorlunda and 1 other person

## 1. What is electrostatic force and how does it relate to current in a circuit?

Electrostatic force is a type of force that exists between electrically charged particles. In a circuit, this force can cause charged particles to move, creating an electric current.

## 2. How does the presence of charged particles affect the electrostatic force in a circuit?

The presence of charged particles, such as electrons, in a circuit creates an imbalance of charges. This imbalance leads to the attraction or repulsion of particles, resulting in the electrostatic force that can create current.

## 3. Can electrostatic force exist in a circuit with no current?

Yes, electrostatic force can exist in a circuit with no current if there is a buildup of static electricity. This occurs when there is an excess of charged particles in one area, but no movement or flow of these particles.

## 4. How does the strength of the electrostatic force affect the amount of current in a circuit?

The strength of the electrostatic force is directly related to the amount of current in a circuit. A stronger force will result in a greater movement of charged particles and therefore a higher current. A weaker force will result in a lower current.

## 5. Can the electrostatic force be controlled or manipulated in a circuit?

Yes, the electrostatic force can be controlled and manipulated in a circuit through the use of different materials and components. For example, insulators can help to prevent the buildup of static electricity, while conductors can help to facilitate the flow of current.