# Net charge VS dipole moment in E field by infinite line charge

1. Jan 20, 2004

### yanyin

could anyone compare the behaviors of (1) an object with a net charge but no dipole moment and (2) an object with net charge but with a dipole moment when placed in the electric field produced by an INFINITE line charge?
thankyou

2. Jan 21, 2004

### Chi Meson

The charged object will experience a force (Coulomb force) that is perpendicular to the wire.

THe object that has a dipole moment will feel the same force, but as it moves, it will feel a second force (Lorentz force)that is parallel to the wire.

Edit: this second force depends on the orientation of the dipole: the north-south axis should be perpendicular to the wire AND perpendicular to a line that is drawn radially from the wire.

Edit Edit: No, no, Ignore that last edit, it's wrong. I just sprained my right hand trying to figure out these directions.

Last edited: Jan 22, 2004
3. Jan 21, 2004

### turin

The E-field can induce a torque on (2), but it cannot do so on (1).

4. Jan 21, 2004

### Chi Meson

Re: Re: net charge VS dipole moment in E field by infinite line charge

Hmm, torque....the net force Lorents is zero here? Since the E-Field produced by the line charge is not uniform, wouldn't the force produced on the near side of the dipole be greater?

5. Jan 22, 2004

### Chi Meson

I lost sleep last night trying to figure it out, and I am seeing it Turin's way now, but help me out here:

What is the shape of the magnetic field produced by a infinite line charge that is moving away (in a direction along a perpendicular from the line-charge). (THis is what the dipole would "obseve" if it and line were charged alike)

As I'm seeing it, there is no net magnetic field in the plane of motion of the line, while above and below the line the magnetic file runs parallel to the line (opposite directions above and below).

IS this correct or even close?

6. Jan 22, 2004

### turin

Sorry, I didn't mean to cause confusion. I didn't mean torque exclusively. If you wanted to break the motivation into a translational term and a rotational term, then the dipole would have a rotational term, whereas the charge distribution lacking a dipole moment would not. That's all I'm saying. Of course, whether or not a dipole moment exists is a matter of perspective. It depends on the center of reference. IMO, the least ambiguous assumption is to consider moments about the center of mass of the charge distribution.

I didn't consider the relativistic effects. I just assumed a static case. But I agree that this is relevent.

This sounds reasonable. I don't think that there should be a magnetic field in the direction of movement, which would correspond to the plane through which the line moves. I was going to try to calculate it exactly, but I don't think I want to now. I came up with this for the charge-current density 4-vector (assuming a line charge that starts on the z-axis at t = 0 and moves in the x-direction at speed v):

j0 = &lambda;'c&delta;(x-vt)&delta;(y)
j1 = &lambda;'v&delta;(x-vt)&delta;(y)
j2 = 0
j3 = 0

Of course, v would not be a constant. That is what makes me skeptical.