# Electric field due to current carrying conductor

Does static charge near to a constant current carrying conductor experience force on it?
I am asking this question because i have learned that electric field and mangnetic field are same thing but viewing differently with respect to the frame of reference...when a positive test charge moves ( parallel to the wire) near to the current carrying conductor ,with respect to the positive charge positive ions in the conductor are moving and due to length contraction charge density due to positive ions will be higher so net electric field will be present. that will repel the test charge... So magnetic field in the rest frame is actually electric field in the test charge's moving frame..i am ok with this .but consider when that test charge at stationary position ,it sees the length contraction of electrons ( which are moving) ... So there will be an attractive electrical force ....but if I think like the following,wire is actually neutral because at a time,number of electrons enter in to the wire equal to number of electrons leave ...so in that way static test charge will not experience any force. I feel contradiction...help me

I am repeating my question, electric field due to current carrying conductor is zero or not??

Last edited by a moderator:

Dale
Mentor
2020 Award
I am repeating my question, electric field due to current carrying conductor is zero or not??
For an ideal conductor it is zero. Real conductors may be slightly non zero, but for all practical purposes (including relativistic effects) you can consider it zero for a good conductor.

How familiar are you with four-vectors. The easiest explanation uses them.

Jano L.
Gold Member
Does static charge near to a constant current carrying conductor experience force on it?

...but consider when that test charge at stationary position ,it sees the length contraction of electrons ( which are moving) ... So there will be an attractive electrical force ....but if I think like the following,wire is actually neutral because at a time,number of electrons enter in to the wire equal to number of electrons leave ...so in that way static test charge will not experience any force. I feel contradiction...help me

I am repeating my question, electric field due to current carrying conductor is zero or not??

It is not zero in general, and can be quite measurable, indirectly, as electric potential that decreases the farther from the wire you go. The direction of this field when near the wire is along the wire, when farther from wire, more radial and hard to determine - it depends on the objects in the vicinity of the wire.

The relativistic contraction of lengths does not mean that density of negative charge is necessarily higher than density of positive nuclei. The interior of the wire is to a high accuracy neutral, since any local excess is electrostatically unstable and is quickly disrupted by movable electrons from the surrounding metal.

The major effect on the electric field outside the wire is due the same charges that produce electric field inside the wire - the charges on the surface of the wire. The surface of the wire is a boundary that the charges cannot easily cross so accumulation and excess of charges can persist there. And it has to, if there is to be non-zero electric field inside the wire. These charges have nothing to do with contraction of lengths, but everything to do with resistance of the wire. For same current and wire diameter, the higher the resistance of the wire, the greater the density of surface charges.