Solving Two Point Dipoles - Find Torque of p1 & p2

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SUMMARY

The discussion focuses on calculating the torque of two point dipoles, p1 and p2, which are positioned at a distance r apart and oriented perpendicularly. The torque is determined using the formula τ = p × E, where E is the electric field generated by the dipole. The electric field for a point dipole oriented in the z direction is given by E_dip = (1/(4πε))(p/r^3)[2cos(θ) r^ + sin(θ) θ^]. The participants emphasize that both torques can be computed easily by rotating the coordinate system, but caution against overlooking the relative differences in answers when doing so.

PREREQUISITES
  • Understanding of point dipoles and their properties
  • Familiarity with torque calculations in physics
  • Knowledge of electric fields generated by dipoles
  • Basic grasp of coordinate transformations in physics
NEXT STEPS
  • Study the derivation of the electric field for point dipoles in various orientations
  • Learn about the conservation of angular momentum in dipole interactions
  • Explore the implications of Newton's third law in electromagnetic systems
  • Investigate coordinate transformations and their effects on physical calculations
USEFUL FOR

This discussion is beneficial for physics students, particularly those studying electromagnetism, as well as educators and researchers interested in the dynamics of dipole interactions and torque calculations.

Kolahal Bhattacharya
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Homework Statement


Griffiths offers this problem: two point dipoles p1 and p2 are given.They are r distance away and they are perpendicular.We are asked to find torue of p1 (about p1's centre) due to p2 and vice versa.
Well, the situation is that I knoe it is =p cross E
even I know the formula for a point dipole pointing in the z direction:
E_dip=(1/(4*pi*epsilon))(p/r^3)[2cos(theta) (r^)+sin (theta) (theta^)
where (r^) and (theta^) are the unit vectors in a polar system coincident with the xyz system.
I can surely find the result for 1 part.Assuming p1 points in the z direction,it can be evaluated.What could be done in the second case?


Homework Equations





The Attempt at a Solution

 
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Both torques are equally easy to compute. Just rotate your coordinate system. But you don't even have to. Their sum is the time rate of change of angular momentum, a conserved quantity. Think Newton's third law.
 
Last edited:
You are WRONG.If I rotate the axes,the relative difference of answers will not be visible.
 
Kolahal Bhattacharya said:
You are WRONG.If I rotate the axes,the relative difference of answers will not be visible.

Really? I have no idea what you mean to say, but I guess you know best.
 

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