A positive point charge (+q) is kept in the vicinity of an uncharged conducting plate. Sketch electric field lines originating from the point on to the surface of the plate.
Derive the expression for the electric field at the surface of a charged conductor.

Explanation

Representation of electric field : The electric field due to a positive charge (+q) is represented as in fig.
Electric field due to a point charge : Consider a point charge +q placed at the origin O of the coordinate frame. Let `q_(0)` be any test charge placed at P.
According to Coulomb's Law, force on the test charge `q_(0)` due to charge q is given by
`vec(F)=1/(4 pi in_(0)) (q q_(0))/r^(2) hat(r)`
where `hat(r)` is a unit vector along OP. If `vec(E)` be the electric field at point P then

`vec(E)=F/q_(0)=1/(4pi in_(0)) 1/r^(2) hat(r)`
`vec(E)=1/(4pi in_(0)) q/r^(3). vec(r)" "[ :' hat(r)= vec(r)/(|r|)]`
`:.` The magnitude of the electric field at point P is given by
`E=1/(4 pi in_(0)). q/r^(2)`
The electric field due to a point charge is spherical symmetric about the charge.