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

AI Thread Summary
To find the electric field at a corner of a square with side length a and charge q, breaking the problem into components is the standard approach. While the discussion suggests exploring simpler methods using basic linear algebra, it concludes that no straightforward trick exists for this scenario. The complexity of the electric field calculations often necessitates component addition to determine the resultant field accurately. This method is essential for both square and cube configurations. Ultimately, mastering component analysis is crucial for solving electric field problems effectively.
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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