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

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To calculate the force holding two halves of a charged sphere together, one can use Coulomb's law, which is expressed as F = (1/4πε₀) * (q₁q₂/r²). The discussion suggests exploring alternative methods, such as computing the electromagnetic stress tensor derived from the field strength. Integrating this tensor over a strategically chosen surface may provide a simpler solution than traditional calculus methods. Participants are encouraged to share their experiences or insights regarding these approaches. The conversation emphasizes finding efficient calculation methods for this physics problem.
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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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