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debkar
debkar is offline
#27
Aug9-10, 08:35 AM
P: 2
Hey i have a new proof of gauss law.now i am listing it below

let there be an arbitaraly shaped body.let there be a charge Q,e='epsilon not',E=electric field,dS=small surface element.
let the body be consisting of many small surface elements dS1,dS2......
let the individual surfaces be so small that radius here are constant and be r1,r2......... respectively
therefore surface integral of E.dS=E1.dS1+E2.dS2+.....
since theta =0 therefore E.dS=E*dS

therefore putting values

Q*dS1/(4*pi*e*r12)+Q*dS2/(4*pi*e*r22)+....

d(theta1)=dS1/dr12,d(theta2)=dS2/dr22,etc (from definition of solid angle)

taking everything in common


net elctric flux=Q/(4*pi*e)(dS1/dr12+dS2/dr22+...)
=Q/(4*pi*e)(d(theta1)+d(theta2)+....)
=Q/(4*pi*e)(4*pi)=Q/(e)
(since sum of all solid angle around the charge is 4*pi)