# I The force between a stationary and a mobile charge

1. Aug 11, 2017

### hokhani

Does a current (or a mobile charge) exert any force on the stationary charge (charge with no motion)? We know that the current produces a magnetic field around which exert a magnetic force on mobile charge and now I like to know whether the current exert force on a stationary charge.

2. Aug 11, 2017

### Orodruin

Staff Emeritus
The electromagnetic force on a stationary charge is independent of the magnetic field. Only the electric field is relevant.

3. Aug 11, 2017

### hokhani

Do you mean that the two currents also exert electric field as well as magnetic field?

4. Aug 11, 2017

### Staff: Mentor

A current through a wire, where the electric forces are neutralized, exerts no electric force on the particle. Hence why it doesn't move. However, a lone charge passing by the stationary charge does not have its electric field canceled by opposite charges and the stationary charge will feel an electric force from the moving charge.

5. Aug 12, 2017

### hokhani

As far as I understand, you say that a current in a wire doesn't exert any electric force on an electric charge located around the wire because the electric in the wire is neutralized. Could you please explain further why and how the electric field is neutralized?
You said that instead, a moving charge exerts an electric force on another charge around it. How about two moving charges? Do they exert both electric and magnetic forces on each other?

6. Aug 12, 2017

### Ibix

There are the same number of electrons and protons in the wire. There is a net charge of zero and therefore a net electric field of zero. But there's a magnetic field if there is a current flowing. This is different from a free charge or an electron beam or something of that nature.
Depends on their state of motion with respect to one another and the frame you analyse them in. Two charges in motion in your frame will have both electric and magnetic fields and will both affect the other with them.

7. Aug 12, 2017

### Staff: Mentor

What Ibix said.

8. Aug 14, 2017

### hokhani

According to one of the Maxwell equations, namely $$\nabla \times B=J+\frac {\partial D} {\partial t},$$ both current and the change of electric field can generate magnetic field. So your above statement implies that there are two portions of magnetic field for a dynamic charge (charge in motion): one due to the current it produces and the other due to the change of the electric field caused by the motion of charge. Could you please correct me if I am wrong?

9. Aug 14, 2017

### Ibix

The current density associated with a moving charge is zero everywhere except where there is charge. So everywhere except inside the charge, the fields satisfy $\nabla\times B=\partial D/\partial t$. Inside the charge, there is a contribution to the curl of the magnetic field from the current density, yes. I am not sure without doing more maths whether that means you can always separate the magnetic field into a contribution from the changing electric field and a contribution from the current.

Note that "inside the charge" may or may not make sense, depending on exactly what model of a charge you are using.