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Consider the following statements about electric dipole and select the correct ones. S1 : Electric dipole moment vector \[\overset{\to }{\mathop{p}}\,\]is directed from the negative charge to the positive charge 52 : The electric field of a dipole at a point with position vector \[\overset{\to }{\mathop{r}}\,\] depends on \[\overset{\to }{\mathop{\left| \text{r} \right|}}\,\] as well as the angle between r and p.  The electric dipole potential falls off as \[\frac{1}{{{r}^{2}}}\]  and not as \[\frac{1}{r}.\] S4: In a uniform electric field, the electric dipole experiences no net forces but a torque \[\overset{\to }{\mathop{\text{t}}}\,=\overset{\to }{\mathop{\text{p}}}\,\text{ x }\overset{\to }{\mathop{\text{E}}}\,.\]

A)  S2, S3 and S4   

B)  S3 and S4

C)  S2 and S3           

D)  All four

Correct Answer: D

Solution :

                 (i) An electric dipole is a pair of equal and opposite charges q and - q separated by same distance 2\[l\].                            (ii) The electric field due to a dipole at a point P is                 \[E=\frac{p}{4\pi {{\varepsilon }_{0}}}\frac{\sqrt{3{{\cos }^{2}}\theta +1}}{{{r}^{3}}}\]    \[(r>>a)\] (iii) The electric potential due to dipole in its general position is given by                 \[V=\frac{k\,.\,\,p\cos \theta }{{{r}^{2}}}\]                 \[V\propto \frac{1}{{{r}^{2}}}\] So, the electric dipole potential falls off as \[\frac{1}{{{r}^{2}}}\]and not as \[\frac{1}{r}\]. (iv) In a uniform electric field, the electric dipole experiences no net force but a torque    \[\tau =\vec{p}\times \vec{E}\]