Define electric flux. Give its SI unit. Using Gauss. law, deduce an expression for the electric field due to a uniformly charged spherical conducting shell of radius R at a point
outside

Explanation

Electric flux
Electric field due to a uniformly charged spherical conducting shell Let `sigma` be the uniform surface charge density of a thin spherical shell of radius R. The Gaussian surface will be a spherical surface centred at the centre of shell.
At a point outside the shell, `(r gt R)` Since, E and dS are in the same direction,
`therefore phi_(E)= underset(S)oint E.dS= (q)/(epsi_(0))`
`rArr phi_(E)= E underset(S)oint dS= (q)/(epsi_(0))`
or `E(4pi r^(2))= (q)/(epsi_(0)) rArr E= (q)/(4pi epsi_(0)r^(2))`
Since, `q= sigma xx 4pi R^(2) rArr E= (sigma R^(2))/(epsi_(0)r^(2))`
Vectorially, `E= (sigma R^(2))/(epsi_(0)r^(2))hat(r )`