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 * 1 0 − 6 C m , is ±9*103 V . (Take 1 4 π ϵ 0 = 9 * 1 0 9 SI units) Reason R : V = ± 2 P 4 π ? 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 potential V at any point, at distance r from centre of dipole = KPcosθ r 2 At axial point where θ=0? , V=KPr2=9*109*4*10−622=9*103 V At axial point where θ=180? , V=−KPr2=−9*103 V

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 $\dot{P}$ of magnitude, $4 * 1 0^{- 6} C m$ , is $\pm 9 * 1 0^{3} V$ .

**(Take $\frac{1}{4 π ϵ_{0}} = 9 * 1 0^{9}$ SI units)

Reason R : $V = \pm \frac{2 P}{4 π ?_{0} r^{2}}$ , 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:**

Option 1 - Both <math> <mrow> <mi>A</mi> </mrow> </math> and <math> <mrow> <mi>R</mi> </mrow> </math> are true and <math> <mrow> <mi>R</mi> </mrow> </math> is the correct explanation of <math> <mrow> <mi>A</mi> </mrow> </math> .

Option 2 - Both <math> <mrow> <mi>A</mi> </mrow> </math> and <math> <mrow> <mi>R</mi> </mrow> </math> are true and <math> <mrow> <mi>R</mi> </mrow> </math> is NOT the correct explanation of <math> <mrow> <mi>A</mi> </mrow> </math> .

Option 3 - <math> <mrow> <mi>A</mi> </mrow> </math> is true but <math> <mrow> <mi>R</mi> </mrow> </math>  is false.

Option 4 - <math> <mrow> <mi>A</mi> </mrow> </math> is false but <math> <mrow> <mi>R</mi> </mrow> </math>  is true.

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Answered by

Alok Kumar Singh | Contributor-Level 10

6 months ago

Correct Option - 3

Detailed Solution:

The potential $V$ at any point, at distance $r$ from centre of dipole $= \frac{K P cos θ}{r^{2}}$