# Griffiths Problem 4.8

1. Apr 6, 2008

### ehrenfest

[SOLVED] Griffiths Problem 4.8

1. The problem statement, all variables and given/known data
This question refers to Griffiths E and M book.

Why is the answer not 2 times that?
Why don't you need to add the energy of dipole 1 to the energy of dipole 2 like

$$\bf -p_1 \cdot E_2 - p_2 \cdot E_1$$

?

2. Relevant equations

3. The attempt at a solution

2. Apr 6, 2008

### nrqed

For the same reason that the potential energy of a pair of two point charges is k q_1 q_2/r.

Imagine assembling the system, starting with the two dipoles at infinite distances. Bringing the first dipole from infinity requires no energy. Bringing the second dipole from infinity (while holding the first one at rest) requires an energy equal to - p2 dot E_1. That's the total energy stored in the system since it's the total energy that was required to assemble the system

3. Apr 9, 2008

### ehrenfest

But it also requires energy to hold the first dipole at rest, doesn't it? Well I guess there is no work done doing that. But it seems like you don't get that for free!

Last edited: Apr 9, 2008
4. Apr 9, 2008

### nrqed

as you say, there is no work involved doing that. I know what you mean but there is a very clear definition of work in physics and we have to stick to it.