Can Coulomb's Law be Simplified for Finding Electric Field at Corners?

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SUMMARY

The discussion focuses on calculating the electric field at the corners of a square with side length 'a' and point charges 'q' using Coulomb's Law. While the user inquires about simplifying the process through linear algebra, the consensus is that breaking the electric field into components remains the most effective method. There are no shortcuts identified for calculating the electric field at corners of a square or cube, emphasizing the necessity of component addition in these scenarios.

PREREQUISITES
  • Coulomb's Law for electric fields
  • Basic linear algebra concepts
  • Vector addition techniques
  • Understanding of electric field vectors
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  • Study vector addition in the context of electric fields
  • Explore advanced applications of Coulomb's Law
  • Learn about electric field calculations in three-dimensional geometries
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Physics students, electrical engineers, and anyone interested in electrostatics and electric field calculations.

NotMrX
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Hello,

I was wondering if we had a square with side length a and charges q. What would be the electric field at a corner? I can work this out by breaking stuff into components but I wondered if there was an easier way using very basic linear algebra. What about a cube? In other words are there any tricks to make it easier rather than just break it into components, add them, and find the resultant?
 
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It's not clear from your problem statement where the charge is with respect to the square, but my guess is that there is not a simple trick available. Adding components is something you will do a lot.
 

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