Uniformly Polarized disk on a conducting plane (E-Field)

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SUMMARY

The discussion focuses on calculating the electric field intensity vector along the z-axis for a uniformly polarized dielectric disk positioned on a conducting plane. The polarization vector is defined as P = P \hat{k}, with the disk having a radius a and thickness d. Participants compare their solutions, confirming that while the electric field components E1(z) and E2(z) are correct, the simplification process was not effectively executed, leading to unnecessary complexity in the final expressions.

PREREQUISITES
  • Understanding of electric fields and polarization in dielectrics
  • Familiarity with boundary conditions for electric fields at conducting surfaces
  • Knowledge of vector calculus, particularly in three-dimensional space
  • Basic principles of electrostatics and dielectric materials
NEXT STEPS
  • Study the derivation of electric fields from polarized dielectrics
  • Learn about boundary value problems in electrostatics
  • Explore simplification techniques for vector equations in electromagnetism
  • Investigate the effects of dielectric materials on electric field distribution
USEFUL FOR

This discussion is beneficial for physics students, electrical engineers, and researchers focusing on electrostatics, particularly those dealing with dielectric materials and their interactions with conductive surfaces.

jegues
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Homework Statement



A uniformly polarized dielectric disk surrounded by air is lying at a conducting plane, as shown in the figure. The polarization vector in the is,

[tex]\vec{P} = P \hat{k},[/tex]

the disk radius is a, and the thickness d. Calculate the electric field intensity vector along the disk axis normal to the conducting plane (z-axis).

Homework Equations





The Attempt at a Solution



See the second figure attached for their solution and a picture of the problem, and the first figure for my attempt.

Are our answers the same? I can't seem to get it exactly in the form they have but it looks relatively close.

Can someone confirm?
Is my answer equivalent to theirs? If no what did I do wrong?
 

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your E1(z) is ok, your E2(z) is ok. your re-writing of them , as they are added, makes them seem more complicated, rather than terms canceling (to simplify).
 

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