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

In summary: Originally posted by Chi Meson ... 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? It looks like this vector would be pointing in the opposite direction of the magnetic field produced by the line charge.
  • #1
yanyin
21
0
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
 
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  • #2
Originally posted by 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

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:
  • #3
Originally posted by 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?
The E-field can induce a torque on (2), but it cannot do so on (1).
 
  • #4


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

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
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
Originally posted by Chi Meson
Hmm, torque...the net force Lorents is zero here?
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.




Originally posted by Chi Meson
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)
I didn't consider the relativistic effects. I just assumed a static case. But I agree that this is relevent.




Originally posted by Chi Meson
... 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?
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 = λ'cδ(x-vt)δ(y)
j1 = λ'vδ(x-vt)δ(y)
j2 = 0
j3 = 0

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

1. What is the difference between net charge and dipole moment?

Net charge refers to the overall charge of an object or system, while dipole moment measures the separation of positive and negative charges within an object. Net charge is a scalar quantity, while dipole moment is a vector quantity.

2. How does an infinite line charge affect the electric field?

An infinite line charge creates a radial electric field around it, meaning the electric field lines point away from the charge in all directions. The strength of the electric field decreases as the distance from the line charge increases.

3. Is the net charge of an infinite line charge zero?

Yes, the net charge of an infinite line charge is zero because the positive and negative charges are equally distributed along the line, creating a neutral overall charge.

4. How does the dipole moment of an infinite line charge change with distance?

The dipole moment of an infinite line charge remains constant regardless of distance from the line. This is because the separation of charges within the line is constant and does not change with distance.

5. Can an infinite line charge have a non-zero net charge?

No, an infinite line charge cannot have a non-zero net charge. As mentioned earlier, the positive and negative charges are equally distributed along the line, resulting in a net charge of zero.

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