Consider an infinitely long straight line carrying uniform line charge with density and lies on Z-axis from to .
Consider a point P at which Electric field intensity has to be determined which is produced by the line charge distribution.
from the figure let the co-ordinates of P are ( a point on y-axis) and assume is a small differential charge confirmed to a point M as co-ordinates.
produces a differential field
the position vector and the corresponding unit vector
then the Electric field strength produced by the infinite line charge distribution is
to solve this integral let
is a function of only, there is no component and is the perpendicular distance from the point P to line charge distribution .