A linear positive charge distribution, with linear charge density $$\lambda$$ coulomb per meter, extends along positive $$x$$ axis from $$x = 0$$ to $$x = \infty$$. The electric field $$E$$ at any point $$P\,(0,y)$$ on the $$y$$ axis

A

is proportional to $$\frac{\lambda}{y^2}$$ irrespective of whether $$y$$ is positive or negative

B

is always directed away and perpendicular to the line of charge

C

has a vanishing component parallel to the line of charge

D

is directed along a straight line of slope $$m = -1$$ if $$y$$ is positive but along a line of slope $$m = +1$$ if $$y$$ is negative