# B Electric field of a moving charge?

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1. Apr 9, 2017

### Cozma Alex

I have a moving charge in a generic motion, and I pick a point p, how do I get the electric field caused by the charge on point p, at any time?
Can I use the coulomb definition of electric field that relates it's strenght with the Distance?
Or does that law works only when the charge is static?
How can I Do?
Btw this is not a homework question oregarding something, i'm just wondering cause I never encountered such a problem and they told me that coulomb law work for electrostatics

I know all maxwell equations

2. Apr 9, 2017

### QuantumQuest

First, I have to tell you that in order to calculate the fields (electric and magnetic) of a moving charge , the math are somewhat involved. You can derive the fields from the (retarded) potentials. For a such derivation you can take a look here. Also, for a derivation using first principles take a look here.

3. Apr 9, 2017

### Cozma Alex

What are the retarded Potential? Why can't I use the coulomb Law?
The magnetic field is not conservative, how can it have a Potential?

4. Apr 9, 2017

### QuantumQuest

Retarded potentials are the electromagnetic potentials generated by time-varying electric current or charge distributions in the past. For more see Wikipedia.

Coulomb's Law can be applied for static charge(s) or in integral form for charge distributions. Now, if we have a moving charge we have a magnetic force as well. So, we can't consider only the electrostatic force in this case.

The magnetic field itself is neither conservative nor non-conservative. In order to characterize a field in general as conservative or not, you have to take the force applied on a particle moving along any closed path and calculate the net work done. But in this case, the magnetic field (effectively force) on a moving particle is at right angles to the motion so the work is always zero. So, there is no proper application of the concept.

Last edited: Apr 9, 2017