Torque on Dipole Griffith EM 4.5 p. 165

In summary, Griffith's E&M problem 4.5 on page 165 discusses the torque on p1 and p2, two perfect dipoles located a distance r apart. The torque on p1 due to p2 is found to be along the -x direction, while the torque on p2 due to p1 is along the -x direction as well. The magnitude of the torque is proportional to the product of the two dipole moments and inversely proportional to the cube of the distance between them.
  • #1
stunner5000pt
1,461
2
Griffith's E&M problem 4.5 page 165

In the figure p1 and p2 are perfect dipoles a disantce r apart. What is the torque on p1 due to p2.? Wjat is the torque on p2 due to p1?
the second part is done in post #4
p1 is located on the right pointing upward
p2 is a distance r from p2 and is oriented poitning right

ok first of all the field at p2 due to p1 is

[tex] E = \frac{1}}{4 \pi \epsilon_{0} r^3} (3(\vec{p}\bullet\hat{r})-\vec{p}) = \frac{p_{1}}{4 \pi \epsilon_{0} r^3} (3pr\cos\theta - p)[/tex]

theta is pi/2 so
[tex]E = \frac{-p_{1}}{4 \pi \epsilon_{0} r^3} [/tex]

then the magnitude of torque on p2 is
[tex] N = p_{2} \times \frac{-p_{1}}{4 \pi \epsilon_{0} r^3} [/tex]

p2 points in the y
p1 in teh z
y cross z is positive x
is this correct??
 

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  • #2
Looks mostly right. Two small comments:
1) you left out an r-hat in the first equation
2) y cross z is plus x as you say but E has a minus sign so torque is along -x
 
  • #3
marcusl said:
Looks mostly right. Two small comments:
1) you left out an r-hat in the first equation
2) y cross z is plus x as you say but E has a minus sign so torque is along -x

good point i forgot about hte minus sign
it is -x

thanks a lot!
 
  • #4
this time r points to the left (correct?)
so the angle between p2 and r is -pi? [tex] E =\frac{p_{1}}{4 \pi \epsilon_{0} r^3} (3(\vec{p_{2}}\bullet\hat{-r} \cos\theta - \vec{p}) = \frac{p_{1}}{4 \pi \epsilon_{0} r^3} (-3p_{2}r\cos\theta - \vec{p_{2}}) = \frac{1}{4 \pi \epsilon_{0} r^3} 2p_{2}[/tex]

is that correct? the electric field points to the right??

now let s see if that makes snese intuitively

suppose you are 'behind' the negative charge of a dipole very far away such that r>> d (d is the separation of the dipole) then the electric field due to the two charges points toward the dipole?? because the negative cahrge 'slightly' dominates over the positive charge?

the torque as a result is

[tex] \vec{N} = p_{1} \hat{z} \times \frac{2p_{2}}{4 \pi \epsilon_{0} r^3} \hat{y} = \frac{2p_{1}p_{2}}{4 \pi \epsilon_{0} r^3} (-\hat{x}) [/tex]

the answers are differnet in magnitude but same direction
 
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Related to Torque on Dipole Griffith EM 4.5 p. 165

1. What is torque on a dipole?

Torque on a dipole is the measure of the rotational force applied to a dipole in an electric or magnetic field. It is calculated by multiplying the strength of the field by the distance between the positive and negative charges in the dipole.

2. How is torque on a dipole related to Griffith EM 4.5 p. 165?

In Griffith's Electrodynamics textbook, section 4.5 on dipole fields discusses the calculation of torque on a dipole in an external electric or magnetic field. The equation for torque on a dipole is derived in this section.

3. What factors affect the magnitude of torque on a dipole?

The magnitude of torque on a dipole is affected by the strength of the external electric or magnetic field, the distance between the positive and negative charges in the dipole, and the angle between the dipole moment and the field direction.

4. How is torque on a dipole different from force on a dipole?

Force on a dipole is the linear force exerted on a dipole in an electric or magnetic field, while torque is the rotational force. Force is calculated by multiplying the strength of the field by the dipole moment, while torque also takes into account the distance between the charges in the dipole.

5. What are some real-life examples of torque on a dipole?

Torque on a dipole is observed in many everyday situations, such as a compass needle aligning with the Earth's magnetic field, a motor rotating in an electric field, or the interaction between water molecules in an electric field.

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