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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 `(phi)` through anyt closed surface is `1// in _(0)` times the net charge enclosed by the closed surface.
Expression for electric intensity at a point outside the uniformly chrged shell

Consider a unifomly chrged thin spherical shell of radius R. Let q be the charge distributed on the spherical shell. It produces a spherically symmetric electric firld. Let P be a point distant r from the centre of the shell. To determine the field at P, we imagine a Gaussian sphere of radius r with O as its center as shown in the figure.
The total electric flux through the Gaussian surface3 is given by,
`phi=` Electric field intensity `xx` Area `" "because vecE||vecA`
According to Gauss theore, we have
`phi = (q )/(epsi_(0))`
From equation (1) and (2), we have
`E xx 4pi r ^(2) =(q)/(epsi _(0))`
`E= (q)/(4pi r ^(2) in _(0))`
`E = (1)/( 4pi in _(0)) (q)/(r ^(2))`
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