A point charge +Q is placed at a point. Calculate the electric flux associated with one sphere of radius r , which the given point charge at its centre.

Explanation

Electric lines of forces for point charge are directed radially outwards in all directions. The direction of area segment is also radially outwards. The angle between electric field intensity and area vector at any point of the sphere remains zero, though electric field intensity and area vector both are continuously changing direction from point to point .
Electric flux can be written as follows :
`phi=int_"sphere"vecE.d vecS`
`phi=int_"sphere" EdS cos 0^@=int_"sphere" EdS`
Since the magnitude of `vecE` is same everywhere on a spherical surface, so it can be taken out of the integration :
`phi=E int_"sphere" dS = 1/(4piepsilon_0) Q/r^2 xx 4pir^2`
hence, the electric flux through a spherical surface around point charge at its centre is given by :
`phi=Q/epsilon_0`