How Do You Calculate Torque on a Dipole in a Non-Uniform Electric Field?

[gjfelix2001]

dipole torque problem.. Help please!

Hi, the problem is:

Show that if the force action on a dipole p placed in an Non uniform electric field is $$p\cdot \nabla E_{ext}$$, the torque acting on the dipole in this field is

$$\tau =r \times (p\cdot\nabla E_{ext})+p\times E_{ext}$$

where r is the vector distance to the dipole from the point about which the torque is to be measured.

How can i do this? it's urgent.. please!

 

[Meir Achuz]

The first term is just rXF.
The second term is the torque due to the couple acting on the dipole.
You can get that torque by usilng the couple acting on +q and -q charges
a distance L apart, with p=qL.