Understanding Torque and Cross Product Calculations for Dipoles

[leonne]

Homework Statement

This is a physics problem. need to find torque on dipoles
the
the 2 dipoles are on the same plane with distance r p1 is pointing up while p2 is pointing right

Homework Equations

N=PxE

The Attempt at a Solution

I know how to do a cross product, you make the matrix with xyz, but not sure about this

E=1/(4pieEo r³)[3(p1*r^)r^-p1)

than after the cross product
n=1/(4pieEo r³)[3(p1*r^)p2x r^-p2xp1)
Why is this? Than they go about saying that p1*r^=0 than (p2 x p1^)= p1p2

than the torque on the other particle
n=1/(4pieEo r³)[3(p2*r^)p1x r^-p1xp2)
but this time they saild that (p2*r^)=p

why is p2*r^=p while p1*r^=0?


also this other problem, where it has a point p on z axis and same p2 point on -z axis and ask for torque on p the dipole is pointing perpendicular to the plane in a angle@

n=1/(4pieEo r³)[3(p2*r^)px r^-pxp2)
than somehow they get
n=1/(4pieEo r³)[3(pcos@)(psin@)-p²sin2)

Thanks

 

[ystael]

This is very difficult to read. I'm going to attempt to fill in what the equations should be. Please correct them if they're wrong, and then someone may try to answer. Take a look at the TeX source and you can learn how to type this kind of thing.

Homework Statement

This is a physics problem. need to find torque on dipoles
the
the 2 dipoles are on the same plane with distance r p1 is pointing up while p2 is pointing right

Homework Equations

$$\mathbf{N} = \mathbf{P} \times \mathbf{E}$$

The Attempt at a Solution

I know how to do a cross product, you make the matrix with xyz, but not sure about this

$$\mathbf{E} = \frac1{4\pi\epsilon_0 r^3}(3(\mathbf{p}_1 \cdot \hat{\mathbf{r}})\hat{\mathbf{r}} - \mathbf{p}_1)$$

than after the cross product

$$\mathbf{n} = \frac1{4\pi\epsilon_0 r^3}(3(\mathbf{p}_1 \cdot \hat{\mathbf{r}})\mathbf{p}_2 \times \hat{\mathbf{r}} - \mathbf{p}_2 \times \mathbf{p}_1)$$

Why is this? Than they go about saying that $$\mathbf{p}_1 \cdot \hat{\mathbf{r}} = 0$$ than (p2 x p1^)= p1p2 [I can't tell what this one is supposed to be]

than the torque on the other particle

$$\mathbf{n} = \frac1{4\pi\epsilon_0 r^3}(3(\mathbf{p}_2 \cdot \hat{\mathbf{r}})\mathbf{p}_1 \times \hat{\mathbf{r}} - \mathbf{p}_1 \times \mathbf{p}_2)$$

but this time they saild that $$\mathbf{p}_2 \cdot \hat{\mathbf{r}} = p$$

why is $$\mathbf{p}_2 \cdot \hat{\mathbf{r}} = p$$ while $$\mathbf{p}_1 \cdot \hat{\mathbf{r}} = 0$$?

 

[leonne]

lol thanks