Charge Q is distributed non-uniformly over a ring of radius R, P is a point on the axis of ring at a distance  $\sqrt{3}\mathrm{R}$ from its centre. Which of the following is a wrong statement.

Every point on the ring is at a distance of 2R from the point P,

So the electric potential at P is $\frac{\mathrm{KQ}}{2\mathrm{R}}$

Electric field at a point which is at a distance of x from centre on axis at ring

$=\frac{\mathrm{KQ}\times \mathrm{x}}{{\left({\mathrm{R}}^2+{\mathrm{x}}^2\right)}^{{\displaystyle \raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}}}$

(for uniformly distributed)

$\Rightarrow \mathrm{E}=\frac{\mathrm{KQ}\sqrt{3}\mathrm{R}}{{\left({\mathrm{R}}^2+3{\mathrm{R}}^2\right)}^{3/2}}=\frac{\sqrt{3}\mathrm{KQ}}{8{\mathrm{R}}^2}$But the given ring is non uniformly charged. Hence field can’t be equal to $\frac{\sqrt{3}\mathrm{KQ}}{8{\mathrm{R}}^2}$