Two equal charges q of opposite sign separated by a distance 2a constitute an electric dipole of dipole moment p . If p is a point at a distance r from the centre of the dipole and the line joining the centre of the dipole to this point makes an angle θ with the axis of the dipole, then the potential at P is given by $\large (r > > 2a)$ (Where p=2qa)

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$\large V = \frac{{p\cos \theta }}{{4\pi {\varepsilon _0}{r^2}}}$

$\large V = \frac{{p\cos \theta }}{{4\pi {\varepsilon _0}r}}$

$\large V = \frac{{p\sin \theta }}{{4\pi {\varepsilon _0}r}}$

$\large V = \frac{{p\cos \theta }}{{2\pi {\varepsilon _0}{r^2}}}$

answer is A.

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Detailed Solution

For the given situation, diagram can be drawn as follows. As shown in figure component of dipole moment along the line OP will be . Hence electric potential at point P will be $\large p' = p\cos \theta$ .Hence electric potential at point P will be $\large V = \frac{1}{{4\pi {\varepsilon _0}}}.\frac{{p\cos \theta }}{{{r^2}}}$