Force on point charge caused by another point charge.

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SUMMARY

The discussion focuses on calculating the force between two equal point charges, q, separated by a distance of 2a, using Maxwell’s stress tensor. The formula for the electric field strength, E = 1/(4πε0) * (cos(θ)/r), is derived from the standard electric field equation for point charges, with the cosine component accounting for the geometry of the system. The confusion arises from the diagram depicting opposite charges while the calculations assume both charges are positive. The net electric field direction is clarified to be parallel to the xy plane.

PREREQUISITES
  • Understanding of Maxwell's stress tensor
  • Familiarity with electric field equations for point charges
  • Basic knowledge of vector components in geometry
  • Concept of charge interactions in electrostatics
NEXT STEPS
  • Study Maxwell's stress tensor applications in electrostatics
  • Review electric field calculations for multiple point charges
  • Explore vector decomposition in physics problems
  • Investigate the implications of charge polarity on electric fields
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This discussion is beneficial for physics students, educators, and professionals working in electrostatics, particularly those focusing on electric field calculations and charge interactions.

woprxcpe1704tks
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Homework Statement


Consider two equal point charges q, separated by a distance 2a. Construct the plane equidistant from the two charges. By integrating Maxwell’s stress tensor over this plane, determine the force of one charge on the other.

I have the full solution, but I'm confused on one part. Where does the E=1/4pi...cos(θ)r come from? And by that I mean where does each component come from? I know about the 1/4piε0, but I don't understand the rest.

Full Solution
 
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woprxcpe1704tks said:
Where does the E=1/4pi...cos(θ)r come from?
Apart from the cosine, it is the standard electrical field strength from a point charge. The cosine then evaluates the component perpendicular to the plane.
woprxcpe1704tks said:
And by that I mean where does each component come from?
That follows from geometry.
 
There's a bit of confusion with the diagram which shows opposite signs for the charges, yet the vectors showing the individual fields are for two positive charges. The problem statement and the solution are for charges of the same sign.

Will the net field be parallel to the xy plane or perpendicular to the plane?
 

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