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

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, $4	imes10^{-6}$ C m, is $\pm 9	imes10^3$ V. (Take $1/4\pi\varepsilon_0 = 9	imes10^9$ SI units)
Reason (R): $V = \pm \frac{2P}{4\pi\varepsilon_0 r^2}$, 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:

Accepted Answer

1. **Check Assertion (A):** The electric potential $V$ at an axial point distance $r$ from a short dipole is given by $V = \pm \frac{1}{4\pi\varepsilon_0} \frac{P}{r^2}$.
   Given: $P = 4 	imes 10^{-6}$ Cm, $r = 2$ m, $k = 9 	imes 10^9$ Nm$^2$/C$^2$.
   Calculation: $V = \pm \frac{(9 	imes 10^9)(4 	imes 10^{-6})}{(2)^2} = \pm \frac{36 	imes 10^3}{4} = \pm 9 	imes 10^3$ V. 
   Thus, Assertion (A) is **True**.

2. **Check Reason (R):** The reason statement gives the formula $V = \pm \frac{2P}{4\pi\varepsilon_0 r^2}$.
   The correct formula for potential is $V = \frac{P}{4\pi\varepsilon_0 r^2}$. The factor of 2 in the numerator corresponds to the formula for the *Electric Field* ($E = \frac{2P}{4\pi\varepsilon_0 r^3}$) or is simply incorrect for potential.
   Thus, Reason (R) is **False**.

3. **Conclusion:** (A) is True but (R) is False.

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