Starting from the equations for a dipole oriented along z, show that the field

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SUMMARY

The discussion focuses on deriving the electric field of a perfect dipole oriented along the z-axis, represented by the equation E=[1/(4pi epsilon0 r^3)] [3(p.r-hat)r-hat -p]. The potential V(r) is given as V(r)= (p.r-hat)/(4pi epsilon0 r^2), leading to the electric field E calculated as E=-grad V. The conversation also touches on the relevance of multipole expansion in understanding dipole fields.

PREREQUISITES
  • Understanding of dipole moments in electromagnetism
  • Familiarity with vector calculus, specifically gradient operations
  • Knowledge of electrostatics, particularly the concept of electric potential
  • Basic principles of multipole expansion in physics
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  • Study the derivation of electric fields from potentials in electrostatics
  • Explore the concept of multipole expansion in detail
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  • Investigate the applications of dipole fields in real-world scenarios, such as antenna theory
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Students and professionals in physics, particularly those specializing in electromagnetism, as well as engineers working with electric fields and dipole systems.

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Homework Statement



Starting from the equations for a dipole oriented along z, show that the field of a perfect dipole can be written as:

E=[1/(4pi epsilon0 r^3)] [3(p.r-hat)r-hat -p]

The Attempt at a Solution


V(r)= (p.r-hat)/(4pi epsilon0 r^2)

E=-grad V
=-[3p. r-hat]/[4 pi epsilon0 r^3]
 
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Are you so sure about the grad part?And by the way are you familiar with multipole expansion?
 

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