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State Gauss's theorem. Obtain an express...

State Gauss's theorem. Obtain an expression for elactric field at any point outside a charged spherical hollow conductor (shell).

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Statement : The total electric flux through a closed surface in free space is equal to `1//epsilon_(0)` times the net charge enclosed by the surface . Where `epsilon_(0)` is the absolute permittivity of free space.

The electric flux through the spherical Gaussian surface is given by,
`phi=sum EDeltaScostheta` ... (1)
The angle `theta` between `vecEandDeltaS` is 0 `thereforecos0=1`
from eq . (1) , `phi=sumEDeltaS`.
`phi=EsumDeltaS`
Where `sumDeltaS`= area of the sphercal Gaussian surface
`=4pir^(2)`.
from eq (2), `phi=Exx4pir^(2)`
From Gauss theorem , `phi=(q)/(epsilon_(0))`
On comparing the equations (3) & (4),
`Exx4pir^(2)=(q)/(epsilon_(0))`
`E=(q)/(4piepsilon_(0)r^(2))`
`rArrE=(1)/(4piepsilon_(0))(q)/(r^(2))` 1
This is the expression of electric field due to a point charge . Hence , this shows that entire charge is assumed to be concentrated at the centre of spere .
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