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/eo
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…….qn
Draw imaginary spheres around each charge. Now we make use of the fact that the electric flux through a sphere is q/eo.
Draw imaginary spheres around each charge. Now we make use of the fact that the electric flux through a sphere is q/eo.
Flux due to q1 will be Ø1 = q1/eo
Flux due to q2 will be Ø2 = q2/eo
Flux due to q3 will be Ø3 = q3/eo
Flux due to qn will be Øn = qn/eo
Hence the total flux Øe will be the sum of all flux i.e | |
Ø = Ø1 + Ø2+ Ø3 +Ø4 ……….+ Øn | |
Ø = q1/eo+ q2/eo+ q3/eo+……….. +qn/e | |
Ø = 1/eo(q1+ q2+ q3+……….. +qn) | |
Ø = 1 /eo 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 /eo times the total charge enclosed by the surface. (www.pak-physicsnotes.blogspot.com) |
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