Find the electric field of a point outside sphere

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SUMMARY

The discussion focuses on calculating the electric field of a point outside a sphere without employing Gauss's law. Participants emphasize the need for clarity regarding the type of sphere involved—whether it is imaginary, solid, conducting, or grounded. The use of Coulomb's Law and the spherical coordinate system is highlighted as essential for the calculation. A key insight is the necessity to express the distance from the point to the differential element using the cosine law, particularly when dealing with a spherical shell configuration.

PREREQUISITES
  • Coulomb's Law
  • Spherical Coordinate System
  • Understanding of electric fields
  • Knowledge of geometric relationships in three dimensions
NEXT STEPS
  • Study the method of images for conducting spheres
  • Explore the implications of different types of spheres on electric field calculations
  • Learn to express distances in spherical coordinates using the cosine law
  • Review advanced applications of Coulomb's Law in electrostatics
USEFUL FOR

Physics students, electrical engineers, and anyone interested in electrostatics and electric field calculations outside spherical geometries.

Coderhk
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Homework Statement


Find the electric field of a point outside sphere without using Gauss's law. (Do not evaluate the integral)

Homework Equations


Coulomb's Law
Spherical Co-ordinate System

The Attempt at a Solution


I have attached my attempt as a picture but now I am stuck, I don't know how I can express the distance (h )from the point to the differential element in terms of the other variables. From symmetry I know the y component of the electric field will cancel out
 

Attachments

  • IMG_20190123_000424.jpg
    IMG_20190123_000424.jpg
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Mission impossible without a complete problem statement: what kind of sphere ? Imaginary, solid, conducting, grounded ?
 
BvU said:
Mission impossible without a complete problem statement: what kind of sphere ? Imaginary, solid, conducting, grounded ?
I believe the question is talking about a shpherical shell like a gaussian enclosed sphere. I figured out that I need to express h in terms of the cos law. Thanks.
 
Conducting ? In which case the method of images might help ...
 

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