What is the torque on an electric dipole in an electric field?

Click For Summary
SUMMARY

The torque on an electric dipole in an electric field can be calculated using the formula τ = p × E, where p is the dipole moment and E is the electric field. The net force on the dipole is derived as F = Q²d / (4πε₀R³), indicating that the force is dependent on the charge Q, separation distance d, and radius R. The direction of the force is counter-clockwise (CCW), with the left charge being repulsive and the right charge being attractive, resulting in a net force directed to the left.

PREREQUISITES
  • Understanding of electric dipoles and their properties
  • Familiarity with Coulomb's law and electric fields
  • Knowledge of vector cross products
  • Basic calculus for deriving forces and torques
NEXT STEPS
  • Study the derivation of electric dipole moment and its applications
  • Learn about the behavior of electric fields around dipoles
  • Explore torque calculations in different physical systems
  • Investigate the implications of torque on dipole alignment in external fields
USEFUL FOR

Students in physics, particularly those studying electromagnetism, as well as educators and professionals involved in electrical engineering and applied physics.

says
Messages
585
Reaction score
12

Homework Statement


A charge Q is fixed at the centre of a train track, radius R. An electric dipole with charges Q, -Q, separated by distance d. Show that the net force on the dipole is given by F = Q2d/(4πε0R3)

b) What direction is this force?
c) What is the torque on the dipole?

Homework Equations


F = (1/4*π*ε0) * (Qq/R2)
F = qE+-qE-

The Attempt at a Solution


sinθ = d/2R

F = (Q*Q / 4*π*ε0R2) (d/2R) - (-Q*Q / 4*π*ε0R2) (d/2R)

F = (Q2 d / 8*π*ε0R3) + (Q2 d / 8*π*ε0R3)

F = (2*Q2 d / 8*π*ε0R3)

F = Q2 d / (4*π*ε0R3)

b) The direction of the force is in the counter-clockwise direction (CCW). The charge on the left side of the dipole is repulsive, so it points away from the charge in the middle, while the charge on the right side is attractive, so it points towards the charge. The net force is then pointed towards the left.

c) I'm a bit lost with c) and I'm not really sure where to start. Any guidance would be much appreciated. :)
 

Attachments

  • dipole.png
    dipole.png
    7.9 KB · Views: 429
Last edited:
Physics news on Phys.org
What is the triangle for?
 
The torque on an electric dipole ##\vec{p}## in an electric field ##\vec{E}## is given by ##\vec{\tau}=\vec{p} \times \vec{E}##.
 
  • Like
Likes   Reactions: NFuller

Similar threads

Replies
14
Views
1K
  • · Replies 11 ·
Replies
11
Views
3K
  • · Replies 25 ·
Replies
25
Views
2K
  • · Replies 10 ·
Replies
10
Views
1K
Replies
14
Views
3K
Replies
1
Views
3K
Replies
2
Views
3K
Replies
1
Views
2K
Replies
19
Views
4K