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Column I gives a situation in which two dipoles of dipole moment $p î$ and $\sqrt{3} \hat{p} \hat{j}$ are placed at origin. A circle of radius R with center at the origin is drawn as shown in figure. Column II gives coordinates of certain positions on the circle. Match the statements in column I with the statements in column II.

Column-I

Column-II
(A)
The coordinate(s) of point on circle where potential is maximum.
(p)
$(\frac{R}{2}, \frac{\sqrt{3} R}{2})$
(B)
The coordinate(s) of point on circle where potential is zero.
(q)
$(- \frac{R}{2}, - \frac{\sqrt{3} R}{2})$
(C)
The coordinate(s) of point on circle where magnitude of electric field intensity is $\frac{1}{4 π ε_{0}} \frac{4 p}{R^{3}}$
(r)
$(- \frac{\sqrt{3} R}{2}, \frac{R}{2})$
(D)
The coordinate(s) of point on circle where magnitude of electric field intensity is $\frac{1}{4 π ε_{o}} \frac{2 p}{R^{3}}$
(s)
$(\frac{\sqrt{3} R}{2}, - \frac{R}{2})$
The correct option is:

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(I)-(R, S) (II)-(P) (III)-(R, S) (IV)-(P, Q)

(I)-(P, Q) (II)-(R, S) (III)-(R, S) (IV)-(P)

(I)-(P) (II)-(R, S) (III)-(P, Q) (IV)-(R, S)

(I)-(P) (II)-(P, Q) (III)-(R, S) (IV)-(R, S)

answer is A.

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Detailed Solution

Question Image

$∵ V = \frac{k \vec{p} . \vec{r}}{{| \vec{r} |}^{3}} ∵ | \vec{r} | = R = \cos t$

(I) Hence $V_{\max} \Rightarrow \vec{p} | | \vec{r}$
Hence point $A (\frac{R}{2}, \frac{\sqrt{3} R}{2})$
Ans : I – P
(II) $V_{C} = V_{D} = 0,$ equitorial points C & D
Ans : II – RS
(III) $\frac{k 4 p}{R^{3}} = \frac{k^{2} | \vec{p} |}{R^{3}} \Rightarrow$ at axial points A & B
Ans. III – PQ
(IV) $E = \frac{k 2 p}{R^{3}} = \frac{K | \vec{p} |}{R^{3}}$ point is at equitorial points C & D
Ans : IV – RS

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