How to Calculate the Force Holding Two Halves of a Charged Sphere?

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SUMMARY

The discussion focuses on calculating the force required to hold two halves of a charged metal sphere with radius R and total charge Q. The primary equation referenced is Coulomb's Law, expressed as F = (1/4πε₀) * (q₁q₂/r²). Participants explore alternative methods for calculation, specifically suggesting the use of the electromagnetic stress tensor derived from field strength, which may simplify the process compared to traditional calculus methods.

PREREQUISITES
  • Understanding of Coulomb's Law and electrostatic forces
  • Familiarity with electromagnetic stress tensors
  • Basic calculus and integration techniques
  • Knowledge of electric field concepts and Gauss's Law
NEXT STEPS
  • Research the derivation and application of the electromagnetic stress tensor in electrostatics
  • Study advanced integration techniques for calculating forces in electrostatic systems
  • Explore alternative methods for calculating forces in charged objects beyond Coulomb's Law
  • Learn about Gauss's Law and its implications for electric fields around charged conductors
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Students in physics, electrical engineers, and researchers interested in electrostatics and force calculations in charged systems.

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Homework Statement


A metal sphere of radius R and total charge Q is cut into two equal halves. Find the force that is
necessary to hold the two parts together.

Homework Equations


##F = \frac{1}{4\pi \epsilon _0} \cdot \frac {q_1 q_2}{r^2}##
##\oint \vec E \cdot d \vec A = \frac{q}{\epsilon _0}##

The Attempt at a Solution


Is there any other way which is easy to calculate rather than columb's law (using calculus)?
 
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Have you tried computing the electromagnetic stress tensor from the field strength and integrating it over a "well chosen" surface?
 

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