Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.

Assertion A: The potential (V) at any axial point, at 2 m distance (r) from the centre of the dipole of dipole moment vector P of magnitude, 4 × 10^–6 C m, is ± 9 × 10³ V.

$(\text{Take}\frac{1}{4\mathrm{\pi <!--\; \pi \; -->}{\mathrm{\epsilon <!--\; \epsilon \; -->}}_0}=9\times <!--\; \times \; -->{10}^9\text{SI}\text{Units})$

Reason R: $V=\pm <!--\; \pm \; -->\frac{2P}{4\mathrm{\pi <!--\; \pi \; -->}{\mathrm{\epsilon <!--\; \epsilon \; -->}}_0{r}^2},$where r is the distance of any axial point, situated at 2 m from the centre of the dipole.

In the light of the above statements, choose the correct answer from the options given below:

The correct option is: A is true but R is false.

Let us analyze both the Assertion and the Reason step-by-step:

1. Analysis of Assertion A:
The electric potential ($V$) at an axial point of a short electric dipole at a distance $r$ from its center is given by the formula:
$V=\pm \frac{1}{4\pi {\epsilon }_0}\frac{P}{r^2}$
where:
- $P$ is the magnitude of the dipole moment vector.
- $\frac{1}{4\pi {\epsilon }_0}=9\times {10}^9\text{N m}{²}^{\text{C}}{\mathrm{⁻²}}^{}$ (SI units).
- $P=4\times {10}^{-6}\text{C m}$.
- $r=2\text{m}$.

Substituting these values into the potential formula:
$V=\pm (9\times {10}^9)\times \frac{4\times {10}^{-6}}{2^2}$
$V=\pm (9\times {10}^9)\times \frac{4\times {10}^{-6}}{4}$
$V=\pm 9\times {10}^3\text{V}$
Thus, Assertion A is true.

2. Analysis of Reason R:
The formula given in Reason R is:
$V=\pm \frac{2P}{4\pi {\epsilon }_0{r}^2}$
This formula is incorrect because the factor of 2 in the numerator belongs to the electric field expression along the axial line, not the potential. The correct expression for the electric potential at an axial point of a dipole is:
$V=\pm \frac{P}{4\pi {\epsilon }_0{r}^2}$
Thus, Reason R is false.

Conclusion:
Assertion A is true, but Reason R is false.