Need help with Gradient in Polar Coordinates

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SUMMARY

The discussion focuses on calculating charge density in electromagnetism using the gradient in polar coordinates. The gradient of the electric field E, given as E = kr^3 r^, is derived as 1/r^2 (d/dr)(r^2 Er). The final result for charge density p is established as p = 5kEor^2. This formula is applicable in spherical polar coordinates, emphasizing the importance of understanding the gradient and divergence in this context.

PREREQUISITES
  • Understanding of electromagnetism principles, specifically charge density and electric fields.
  • Familiarity with spherical polar coordinates and their mathematical representation.
  • Knowledge of vector calculus, particularly the concepts of gradient and divergence.
  • Proficiency in using mathematical notation and differentiation techniques.
NEXT STEPS
  • Study the derivation of the gradient in spherical coordinates.
  • Research the concept of divergence in spherical coordinates.
  • Explore the relationship between electric fields and charge density using Gauss's Law.
  • Review vector calculus resources focusing on electromagnetism applications.
USEFUL FOR

Students and professionals in physics, particularly those studying electromagnetism, as well as anyone seeking to deepen their understanding of vector calculus in spherical coordinates.

leonne
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Homework Statement


Well the problem is a electromagnetism problem: I need to find the charge density. Given
E= kr^3 r^


Homework Equations


formula is gradient E=p/e0


The Attempt at a Solution


They got the gradient of E to be 1/r^2 (d/dr) (r^2 Er) i have no idea how they did it i know gradient is d/dx+ d/dy+d/dz so idk how they got that from E

then they got Eo(1/r^2 (d/dr)(r^2(kr^3) ... answer p=5kEor^2

Is that just a formula for any spherical polar coordinate? 1/r^2 (d/dr) (r^2 Er) Professor said something about looking in the back of the front cover for this. I just have pdf of book and doesn't have back cover. So if it is a formula can you tell me the whole thing thanks
 
Physics news on Phys.org
First, ook up the difference between "gradient" and "divergence" :wink:...Then look up "divergence in spherical coordinates".
 

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