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

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

(Take 1/4π∈₀ = 9 × 10⁹SI Units)

Reason (R) :- V = ± (2P/4π∈₀r²), 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 given data are:

• Dipole moment magnitude P = 4 × 10^-6 C·m
• Distance from the centre to the axial point r = 2 m
• 1 / (4π ε₀) = 9 × 10⁹ SI

For a point on the axial line of an electric dipole, the electric potential is

$V\; =\; \backslash frac\{1\}\{4\backslash pi\backslash varepsilon\_0\}\backslash ,\backslash frac\{P\}\{r^\{2\}\}$

Substituting the numbers:

$V\; =\; 9\backslash times10^\{9\}\backslash times\backslash frac\{4\backslash times10^\{-6\}\}\{(2)^\{2\}\}$

Since (2)² = 4, the expression simplifies to

$V\; =\; 9\backslash times10^\{9\}\backslash times\backslash frac\{4\backslash times10^\{-6\}\}\{4\}$

Cancel the factor 4:

$V\; =\; 9\backslash times10^\{9\}\backslash times10^\{-6\}$

Multiplying the powers of ten gives

$V\; =\; 9\backslash times10^\{3\}\backslash \; \backslash text\{V\}$

Because the potential on the axial line can be positive in one direction and negative in the opposite direction, the magnitude is ± 9 × 10³ V, exactly as stated in the Assertion.

Now examine the Reason. It claims

$V\; =\; \backslash pm\backslash frac\{2P\}\{4\backslash pi\backslash varepsilon\_0\backslash ,r^\{2\}\}$

If we evaluate this expression, the extra factor 2 would double the result, giving ± 1.8 × 10⁴ V, which does not match the given value.

Thus the Reason uses an incorrect formula for the axial potential of a dipole.

Consequently:

• Assertion (A) is true.
• Reason (R) is false.

Therefore the correct option is “A is true but R is false.”