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Griffiths torque on a dipole

  • Thread starter ehrenfest
  • Start date
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[SOLVED] Griffiths torque on a dipole

1. Homework Statement
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. Homework Equations



3. The Attempt at a Solution
 

Answers and Replies

kdv
336
1
1. Homework Statement
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. Homework 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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