Homework Help: Griffiths torque on a dipole

ehrenfest · Mar 15, 2008

[SOLVED] Griffiths torque on a dipole

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

In the sentence after equation 4.5, Griffiths says the following:

"For a perfect dipole of infinitesimal length, Eq 4.4 gives the torque about the center of the dipole..."

What is driving me insane is that I thought eqn 4.4 was true precisely when the dipole was finite since they say nothing about d being an infinitesimal there and the vector d sure does not look like an infinitesimal in Figure 4.5!?! I was sure that eqn 4.4 applied only for physical dipoles before I read that sentence! What is wrong here! Please help.

2. Relevant equations

3. The attempt at a solution

kdv · Mar 15, 2008

ehrenfest said: ↑

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

In the sentence after equation 4.5, Griffiths says the following:

"For a perfect dipole of infinitesimal length, Eq 4.4 gives the torque about the center of the dipole..."

What is driving me insane is that I thought eqn 4.4 was true precisely when the dipole was finite since they say nothing about d being an infinitesimal there and the vector d sure does not look like an infinitesimal in Figure 4.5!?! I was sure that eqn 4.4 applied only for physical dipoles before I read that sentence! What is wrong here! Please help.

2. Relevant equations

3. The attempt at a solution

What he does is to do the calculation for a finite [itex] \vec{d} [/itex] in a uniform E field and then consider the limit as d becomes infinitesimal. There is nothing wrong with doing it this way. The only thing is that for an infinitesimal dipole, the product [itex] q \vec{d} [/itex] is not well-defined. But if you introduce a vector [itex] \vec{p} [/itex] for an infinitesimal dipole, then eq 4.5 is completely fine. So the only subtle point i sthe definition of the vector p for a perfet dipole. If it is defined as the infinitesimal limit of the vector "q d" then the whole procedure is well-defined.

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Homework Help: Griffiths torque on a dipole

ehrenfest

kdv