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: B

Solution :

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