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  4. A given charge is situated at a certain distance from an electric dipole in the end on position experience a force F. If the distance of the charge is doubled, the force acting on the charge will be

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Q. A given charge is situated at a certain distance from an electric dipole in the end on position experience a force F. If the distance of the charge is doubled, the force acting on the charge will be

Rajasthan PETRajasthan PET 2005

Solution:

The intensity on axis line of dipole at any point
$ E=\frac{1}{4\pi {{\varepsilon }_{0}}}.\frac{2p}{{{d}^{3}}} $
$ F=qE $ $ =\frac{2qp}{4\pi {{\varepsilon }_{0}}.{{d}^{3}}} $
or $ F\propto \frac{1}{{{d}^{3}}} $
The force at distance 2d from centre
$ F'={{\left( \frac{d}{2d} \right)}^{3}}F $
$ F'=\frac{F}{8} $