GALAXY

GAUSS’S LAW

INTRODUCTION

Gauss’s law is a quantitative relation which applies to any closed hypothetical surface called Gaussian surface to determine the total flux (Ø) through the surface and the net charge(q) enclosed by the surface.

STATEMENT

"The total electric flux through a closed surface is equal to 1/e_o
times the total charge enclosed by the surface."

PROOF

Consider a Gaussian surface as shown below which encloses a number of point charges q₁,q₂,q₃…….q_n
Draw imaginary spheres around each charge. Now we make use of the fact that the electric flux through a sphere is q/e_o

Flux due to q₁ will be Ø₁ = q₁/e_o

Flux due to q₂ will be Ø₂ = q₂/e_o

Flux due to q₃ will be Ø₃ = q₃/e_o

Flux due to q_n will be Ø_n = q_n/e_o

Hence the total flux Øe will be the sum of all flux i.e

Ø = Ø₁ + Ø₂+ Ø_{3 +}Ø₄ ……….+ Ø_n

Ø = q₁/e_o+ q₂/e_o+ q₃/e_o+……….. +q_n/e

Ø = 1/e_o(q₁+ q₂+ q₃+……….. +q_n)

Ø = 1 /e_o  x ( total charge)

This shows that the total electric flux through a closed surface regardless of its shape or size is numerically equal to 1 /e_o times the total charge enclosed by the surface.