Q) Deriving Gauss' Law from Coulomb's Law for a Single Point Charge

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SUMMARY

This discussion focuses on deriving Gauss' Law from Coulomb's Law specifically for a single point charge. The key equation utilized is Coulomb's Law, expressed as F = (k * q1 * q2) / d^2. The goal is to calculate the electric flux through a sphere of radius r surrounding a point charge of magnitude q, using the integral form of Gauss's Law, ∫E * dA = Q/ε°. The challenge lies in transitioning from a volume integral to a surface integral to achieve this derivation.

PREREQUISITES
  • Coulomb's Law and its mathematical formulation
  • Understanding of electric flux and surface integrals
  • Familiarity with Gauss's Law and its integral form
  • Basic knowledge of vector calculus
NEXT STEPS
  • Study the derivation of Gauss's Law from Coulomb's Law in detail
  • Learn about electric flux and its calculation through different surfaces
  • Explore vector calculus techniques relevant to surface and volume integrals
  • Investigate applications of Gauss's Law in electrostatics problems
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Students in physics, particularly those studying electromagnetism, as well as educators and anyone looking to deepen their understanding of the relationship between Coulomb's Law and Gauss's Law.

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Homework Statement


Q) Use Coulomb’s Law to DERIVE the Gauss Law result for the particular case of A
SINGLE POINT CHARGE. That is, using Coulomb’s Law, find the ELECTRIC FLUX going through a sphere of radius r surrounding one point charge of charge-magnitude q.

THANK YOU


Homework Equations


F=((k)(q1)(q2))/d^2

∫E*dA=Q/ε° E and Da are vectors

The Attempt at a Solution


sadly i don't have an attempt because my textbook showes taking Gauss's law and arriving at coulombs law and i can't figure out how to do it in reverse.
 
Physics news on Phys.org
Start by writing out coulombs law as a volume integral - then you need to be able to relate the vlume integral to a surface integral.
 

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