Question

A charge situated at a distance from electric dipole in the end on position experiences a force F. If the distance of the charge is double the the force acting on the charge is what?

Answer 1

$\sf\star\bold\red{\underline{{QUESTION:-}}}$

✓✓A charge situated at a distance from electric dipole in the end on position experiences a force F. If the distance of the charge is double the the force acting on the charge is what?

$\sf\star\bold\green{\underline{{SOLUTION:-}}}$

Let the dipole moment be p and the charge be q placed at the distance r from the dipole.

The electric field due to the dipole at an axial point is

$\sf\:E =\dfrac{1}{4\pi\epsilon_{0}}\times\dfrac{2p}{r^3}$

$\sf\boxed\star\pink{\underline{\underline{{Force\:on\:charge\:q\:at\:a\:distance\:r\:will\:be:-}}}}$

$\sf\:F = qE$

$\sf\:F = q\times\dfrac{1}{4\pi\epsilon_{0}}\times\dfrac{2p}{r^3}$

$\sf\boxed\star\orange{\underline{\underline{{If\: distance\:is\:doubled:-}}}}$

Then,

$\sf\implies\:F'=q\times\dfrac{1}{4\pi\epsilon_{0}}\times\dfrac{2p}{(2r)^3}$

$\sf\green{{\implies\:F'=\dfrac{1}{8}}}$