Potential energy of an electric dipole in electric field

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SUMMARY

The energy of an ideal electric dipole \( p \) in an electric field \( E \) is expressed as \( U = -p \cdot E \). The derivation involves calculating the work done by the torque \( \tau = p \times E \) as the dipole aligns with the electric field. The potential energy depends on the reference point for zero potential energy, which can vary based on the dipole's orientation relative to the electric field. Specifically, if the potential energy is defined as zero when the dipole is perpendicular to the electric field, the integration limits must be adjusted accordingly.

PREREQUISITES
  • Understanding of electric dipoles and their properties
  • Familiarity with vector calculus, specifically dot and cross products
  • Knowledge of torque and its relation to rotational motion
  • Basic principles of electric fields and potential energy
NEXT STEPS
  • Study the derivation of the potential energy of dipoles in varying electric fields
  • Learn about the implications of torque in rotational dynamics
  • Explore the concept of reference points in potential energy calculations
  • Investigate the behavior of dipoles in non-uniform electric fields
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Students of physics, particularly those studying electromagnetism, as well as educators and anyone interested in the dynamics of electric dipoles in electric fields.

Sleepycoaster
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Homework Statement


Show that the energy of an ideal dipole p in an electric field E is given by

U = -p ⋅ E

Homework Equations



Work = θτ where τ is torque

τ = p × E

The Attempt at a Solution



U = ∫(p × E) dθ' (from θ to 0, since the dipole will eventually align itself with the magnetic field.)
=∫pE(sinθ')dθ'
=-pE(cosθ') with limits θ to 0
=-pE + pE(cosθ)
=p ⋅ E - pE

That's not what I needed to prove. Help?
 
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The formula for the potential energy depends where the zero of the PE is placed. The potential energy is the work done by the force when the object moves from the initial position to the position of zero potential. If the potential energy of the dipole is zero when it is perpendicular to the electric field, you have to integrate from θ to pi/2.
 
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ehild said:
The formula for the potential energy depends where the zero of the PE is placed. The potential energy is the work done by the force when the object moves from the initial position to the position of zero potential. If the potential energy of the dipole is zero when it is perpendicular to the electric field, you have to integrate from θ to pi/2.
Okay, thanks!
 

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