• question_answer
                    A point Q lies on die perpendicular bisector of an electrical dipole of dipole moment p. If the distance of Q from the dipole is r (much larger than the size of the dipole) then electric field at Q is proportional to:

    A)                                                                                                                                                                            \[{{p}^{-1}}\] and \[{{r}^{2}}\]   

    B)                 \[p\] and \[{{r}^{-2}}\]                  

    C)                 \[{{p}^{2}}\] and \[{{r}^{-3}}\]                   

    D)                 \[p\] and \[{{r}^{-3}}\]

    Correct Answer: D

    Solution :

                    Electric field due to a dipole at bisector or at a point on its broad side on position is given by                 \[E=\frac{1}{4\,\pi {{\varepsilon }_{0}}}.\frac{p}{{{r}^{3}}}\]                 or            \[E\propto \,\,\frac{p}{{{r}^{3}}}\]                                           ....(i)                 where r is the distance of that point from centre of dipole.                 So, from Eq. (i)                 \[E\propto \,p\]                 and       \[E\propto \,{{r}^{-3}}\]                 Note:    The electric field due to a dipole at its end on position is twice the value at its broad side on position i.e.,                 \[{{E}_{end-on}}=\frac{1}{4\pi {{\varepsilon }_{0}}}\cdot \frac{2p}{{{r}^{3}}}\]

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