Proving Gradient of Electric Field in Coaxial Line Dielectric is 0

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SUMMARY

The discussion centers on proving that the divergence of the electric field (E) in the dielectric of a coaxial line is zero, expressed mathematically as (Grad dot E) = 0. Participants emphasize the application of the divergence theorem to demonstrate this result, clarifying that the divergence operator should be used instead of the gradient operator. The electric field equations specific to coaxial lines are also referenced, highlighting the importance of understanding vector fields in this context.

PREREQUISITES
  • Divergence theorem
  • Understanding of vector fields
  • Electric field equations for coaxial lines
  • Concept of dielectrics in electromagnetism
NEXT STEPS
  • Study the application of the divergence theorem in electromagnetism
  • Learn about the electric field equations specific to coaxial cables
  • Explore the properties of dielectrics and their impact on electric fields
  • Review vector calculus, focusing on divergence and gradient operations
USEFUL FOR

Students and professionals in electrical engineering, particularly those studying electromagnetism and dielectric materials in coaxial systems.

renegade05
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Homework Statement


Show that (Grad dot E) =0 in the dielectric of a coaxial line.
(Hint: apply the divergence theorem to a portion of the dielectric.)

Homework Equations


Divergence theorem

The Attempt at a Solution



I think I need to show that grad dot E = p/epsilon = 0

I don't know - I'm stuck
 
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I think I need to show that grad dot E = p/epsilon = 0
... Well that would be false wouldn't it?
Grad only applies to scalar fields. I think you mean "div" rather than grad.

Do you know the equation for the electric field of a coax line?
Do you know how to find the divergence of a vector field?
 
Apply the divergence theorem --- do EXACTLY what the hint tells you. Simply apply the divergence thm and take Ea to be E from inner surface and Eb to be the E from the outer surface.

Or, since we're probably in the same class read up on the divergence thm and dielectrics from the book.
 

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