Potential of a dipole in E field

  • Thread starter raggle
  • Start date
  • #1
raggle
8
0

Homework Statement



I'm going over some EM notes and I found a derivation for the potential energy of a dipole in an E field which first found the torque on the dipole and then integrated.
I had a go at a derivation that goes the other way, starting from the potential of the 2 charges. I've ran into a bit of a problem midway through and I can't see how to get past it.

Homework Equations



Want to show:
U = -p.E

The Attempt at a Solution


U = q(VB-VA)

now I don't know how to get from here to what I want to show. Both of the potentials look like [itex]\frac{q}{4πε0r}[/itex] , where the r is different in either potential.
The only thing I can think of is to use an approximation to r, but that doesn't give an acosθ term in the numerator.
 

Answers and Replies

  • #2
ehild
Homework Helper
15,543
1,915

Homework Statement



I'm going over some EM notes and I found a derivation for the potential energy of a dipole in an E field which first found the torque on the dipole and then integrated.
I had a go at a derivation that goes the other way, starting from the potential of the 2 charges. I've ran into a bit of a problem midway through and I can't see how to get past it.

Homework Equations



Want to show:
U = -p.E

The Attempt at a Solution


U = q(VB-VA)

now I don't know how to get from here to what I want to show. Both of the potentials look like [itex]\frac{q}{4πε_0 r}[/itex] , where the r is different in either potential.
The only thing I can think of is to use an approximation to r, but that doesn't give an acosθ term in the numerator.

The charges of the dipole are in an external electric field. By changing the angle, that potential energy gained from the field changes, the potential energy of their interaction does not. You ignored the contribution of the external field to the potential energy.

As for the potential energy of the interaction between two point charges, it is [itex]\frac{q_1 q_2}{4 \pi \epsilon_0 r}[/itex] where r is the distance between the charges.

ehild
 

Suggested for: Potential of a dipole in E field

Replies
4
Views
321
Replies
2
Views
161
  • Last Post
Replies
8
Views
605
Replies
43
Views
543
Replies
11
Views
475
Replies
34
Views
1K
  • Last Post
Replies
9
Views
265
Replies
1
Views
228
Replies
14
Views
404
Top