Assertion A: The potential () at any axial point, at 2 m distance () from the centre of the dipole of dipole moment vector of magnitude, C m, is V. Reason R: where is the distance of any axial point, situated at 2 m from the centre of the dipole. [2

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Solution

Q.
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 $\vec{P}$ of magnitude, $4 \times 10^{- 6}$ C m, is $\pm 9 \times 10^{3}$ V.

Reason R: $V = \pm \frac{2 P}{4 π \in_{0} r^{2}},$ 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. [2024]

1 Both A and R are true and R is the correct explanation of A.

2 Both A and R are true and R is NOT the correct explanation of A.

3 A is true but R is false.

4 A is false but R is true.

Ans.
(3)

Potential at any axial point of a dipole is

$V = \pm \frac{| \vec{p} |}{4 π ε_{0} r^{2}}$

$∴$ $V = \pm \frac{4 \times 10^{- 6} \times 9 \times 10^{9}}{{(2)}^{2}} = \pm 9 \times 10^{3}$ $V$

So, assertion is true but reason is false.

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