question_answer

The plates of small size of a parallel plate capacitor are charged as shown. The force on the charged particle of 'q' at a distance \[\ell \] from the capacitor is : (Assume that the distance between the plates is \[d<<\ell )\]

A) Zero                 

B) \[\frac{Qqd}{2\pi {{\in }_{0}}{{\ell }^{3}}}\]

C) \[\frac{Qqd}{\pi {{\in }_{0}}{{\ell }^{3}}}\]                

D) \[\frac{Qqd}{4\pi {{\in }_{0}}{{\ell }^{3}}}\]

Correct Answer: A

Solution :

[B] The two plates acts as a dipole \[\therefore \]Force on charge q; \[F=Eq=\left( \frac{2kQd}{{{\ell }^{3}}} \right).q=\frac{Qqd}{2\pi {{\varepsilon }_{0}}{{\ell }^{3}}}.\]