A charged conducting wire in an electric field

[cosmo123]

Suppose I have a wire with a net charge (lets say negative) in a uniform electric field from another source, such that the field lines are parallel to the wire. I want to work out the electric field surrounding the wire.

Because the wire is conducting, the electric field inside the wire will be zero, because the electric field in the wire causes the charges in the wire to move to cancel it out. Because the exterior electric field also moves the charges around in the wire, this means i can't just add on the field around the wire in equilibrium to the surrounding exterior electric field. I am assuming the charges in the wire get pushed up to each end, but I can't figure out by how much or what field this produces. Any help? :grumpy:

 

[ednobj]

First off, you would definitely need to know the geometry of this wire. Next, the beauty of working with conductors is the ease of the principle of superposition. Basically, solve the problem of the wire without net charge and the electric field and the problem of a non-neutral conductor wire without the external field. Since both solve Poisson's equation with the same boundary conditions (field is zero in the conductor), the solution to your problem is the superposition of those two.

If your initial charge distribution is q1, you will have q1 all along the wire except at the ends you will have q1-q2, and q1+q2 at opposites sides where the charges +/-q2 cancel the external field.