What is the torque on each dipole about its centre in a given electric field?

[rbnphlp]

Homework Statement

Cosnider two dipoles, p1 oriented along z at the origin, and p2 oriented along x at a distance r in the
x - y plane. Given that the torque on a dipole in a field E can be written N = p x E, find the torque on each dipole about its centre.

Homework Equations

N=pxE , E= (p/4ε∏r^3)[2cosθrhat +sinθhat]

The Attempt at a Solution

for p1, I thought , since its on the origin , θ=0 , E=(p/2ε∏r^3)rhat

first of all how do I know which direction is rhat in the x-y-z plane is it just in the z direction? , Now to find
torque = px(p/2ε∏r^3)rhat

and since is the centre of dipole r=r/2

what do you guys think ?
Cheers guys

 

[SammyS]

Homework Statement

Cosnider two dipoles, p1 oriented along z at the origin, and p2 oriented along x at a distance r in the
x - y plane. Given that the torque on a dipole in a field E can be written N = p x E, find the torque on each dipole about its centre.

Homework Equations

N=pxE , E= (p/4ε∏r^3)[2cosθrhat +sinθhat]

The Attempt at a Solution

for p1, I thought , since its on the origin , θ=0 , E=(p/2ε∏r^3)rhat

If you are referring the torque on p₁ due to p₂, then $\hat{r}\$ is $\hat{x}\ .$

first of all how do I know which direction is rhat in the x-y-z plane is it just in the z direction? , Now to find
torque = px(p/2ε∏r^3)rhat

and since is the centre of dipole r=r/2

what do you guys think ?
Cheers guys