How Do You Derive Forces and Couple on an Electric Dipole in an External Field?

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SUMMARY

The discussion centers on deriving the forces and couple acting on an electric dipole with moment p in the presence of a point charge +q. The interaction energy is defined as -pqcos(phi)/4πε0r², where r is the distance and phi is the angle between the dipole moment and the radial vector. Participants seek clarification on deriving the radial force, the force normal to r, and the couple on the dipole, indicating that these can be approached through manipulations of the established energy equation.

PREREQUISITES
  • Understanding of electric dipole moment and its significance.
  • Familiarity with Coulomb's law and electric fields.
  • Knowledge of torque and its relation to rotational motion.
  • Basic proficiency in vector calculus and dot products.
NEXT STEPS
  • Study the derivation of forces on electric dipoles in external fields.
  • Learn about the concept of electric potential and its application to monopoles.
  • Investigate the mathematical treatment of torque in electrostatics.
  • Explore the implications of dipole orientation on interaction energy.
USEFUL FOR

Physics students, electrical engineers, and researchers in electromagnetism seeking to deepen their understanding of electric dipoles and their behavior in external fields.

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Homework Statement


An electric dipole of moment p is placed at a distance r from a point charge +q. The angle between p and r is phi. Show that the energy of interaction between the dipole and the charge is -pqcos(phi)/4\pi\epsilon0r^2

Derive equations for

a)a radial force on the dipole
b)a force on the dipole normal to r
c)a couple on the dipole

Homework Equations


The Attempt at a Solution



I have proved the first part of the question using the integral of the torque between \phi0 and \varphi and setting \varphi0 to 90degrees and I believe that questions a, b and c are simple manipulations of the proved equation, but no book I read will give me a proof or an explanation of the 'radial force' and how to prove questions a, b and c could anyone help?
 
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So you have found the work, or I guess energy of interaction, done to bring the charge to where it is.

a) How would you find the radial force on a monopole? (Hint: potential)
b) Similar idea to a), but different dot product
c) No idea what this means, sorry.
 

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