question_answer

A force of 40 N is acting between two charges in air. If the space between them is filled with glass with \[{{\varepsilon }_{r}}=8\], what will be the force?

A)  15 N                                     

B)  320 N

C)  5 N                                       

D)  32 N

Correct Answer: C

Solution :

                From Coulombs law the force between two charges is \[F=\frac{1}{4\pi {{\varepsilon }_{0}}K}.\frac{{{q}_{1}}{{q}_{2}}}{{{r}^{2}}}\] where r is distance between the charges and K the dielectric constant. In air:     \[{{F}_{1}}=\frac{1}{4\pi {{\varepsilon }_{0}}K}.\frac{{{q}_{1}}{{q}_{2}}}{{{r}^{2}}}=40\,N\] In glass:                 \[{{F}_{2}}=\frac{1}{4\pi {{\varepsilon }_{0}}}.\frac{{{q}_{1}}{{q}_{2}}}{8{{r}^{2}}}\] \[\therefore \]  \[\frac{{{F}_{1}}}{{{F}_{2}}}=\frac{40}{{{F}_{2}}}=8\] \[\Rightarrow \]               \[{{F}_{2}}=5\,N\]