State and prove Gauss Theorem in electrostatics

Gauss’s Theorem Statement:

According to Gauss’s theorem the net-outward normal electric flux through any closed surface of any shape is equivalent to 1/ε0 times the total amount of charge contained within that surface.

Proof of Gauss’s Theorem Statement:

  • Let the charge be = q
  • Let us construct the Gaussian sphere of radius = r

Now, Consider, A surface or area ds having ds (vector)

Normal having the flux at ds:

Flux at ds:

d e = E (vector) d s (vector) cos θ

But , θ = 0

Therefore, Total flux:

C = f d Φ

E 4 π r2


σ = 1 / 4πɛo q / r2 × 4π r2

σ = q / ɛo

Gauss law

According to the Gauss law, the total flux linked with a closed surface is 1/ε0 times the charge enclosed by the closed surface.

\(\begin{array}{l}\oint{\vec{E}.\vec{d}s=\frac{1}{{{\in }_{0}}}q}\end{array} \)

Was this answer helpful?


4 (119)


Choose An Option That Best Describes Your Problem

Thank you. Your Feedback will Help us Serve you better.


  1. Santanu borah Majuli

    Thank you so much

  2. On my online exam this question came and i didn’t study but I got help here
    Thank you

Leave a Comment Cancel reply

Your Mobile number and Email id will not be published.





App Now