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

AI Thread Summary
To derive Gauss' Law from Coulomb's Law for a single point charge, start with Coulomb's Law, which describes the electric force between two charges. The electric field (E) created by a point charge can be expressed as E = k*q/r^2. To find the electric flux through a sphere of radius r surrounding the charge, integrate the electric field over the surface area of the sphere. This involves converting the volume integral of the electric field into a surface integral. Ultimately, this process demonstrates that the total electric flux through the sphere is equal to the charge enclosed divided by the permittivity of free space, confirming Gauss' 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.
 
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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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