Electric PE as a dipole changes its orientation in an electric field

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SUMMARY

The discussion focuses on calculating the change in electric potential energy (ΔU) of an ammonia molecule (NH3) with a dipole moment of 5.0×10−30C⋅m as it transitions from a parallel to a perpendicular orientation in a uniform electric field of 1.0×106N/C. The potential energy of a dipole is defined by the equation U = -p · E, where U is zero when the dipole is perpendicular to the field. The torque on the dipole is given by τ = p × E, leading to the relationship ΔU = -W = -∫θiθf τ dθ for calculating the work done.

PREREQUISITES
  • Understanding of dipole moments and their significance in molecular physics.
  • Familiarity with electric fields and their properties, specifically uniform electric fields.
  • Knowledge of potential energy equations related to electric dipoles.
  • Basic calculus skills for evaluating integrals in physics equations.
NEXT STEPS
  • Study the derivation of the potential energy formula for electric dipoles.
  • Learn about the relationship between torque and potential energy in electric fields.
  • Explore the concept of electric field strength and its effects on molecular orientation.
  • Investigate the applications of dipole moments in molecular chemistry and physics.
USEFUL FOR

This discussion is beneficial for physics students, particularly those studying electromagnetism, as well as educators and researchers interested in molecular interactions in electric fields.

GodPlaysDice
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Homework Statement


The ammonia molecule (NH3) has a dipole moment of 5.0×10−30C⋅m. Ammonia molecules in the gas phase are placed in a uniform electric field E⃗ with magnitude 1.0×106N/C.
What is the change in electric potential energy when the dipole moment of a molecule changes its orientation with respect to E⃗ from parallel to perpendicular?


Homework Equations


V = U/q
ΔU = -integral(qE dl)
ΔV = -integral(E dl)
E(r) = -∇V(r)
I have no idea what the upside down delta is...

The Attempt at a Solution



I don't even know where to start. :confused:
 
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Potential energy of a dipole is given by this formula: $$U = -\stackrel{\rightarrow}{p} \cdot \stackrel{\rightarrow}{E}$$Where U is defined to be zero when the dipole is perpendicular to the field. It's derived from the formula for the torque on the dipole: \tau = \stackrel{\rightarrow}{p} \times \stackrel{\rightarrow}{E}, using the relationship U = -W = -\int^{\theta_{f}}_{\theta_{i}}\tau d\theta
 
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