question_answer

Two point dipoles of dipole moment \[{{\overrightarrow{p}}_{1}}\] and \[{{\overrightarrow{p}}_{2}}\] are at a distances from each other and \[{{\overrightarrow{p}}_{1}}||{{\overrightarrow{p}}_{2}}.\] The force between the dipoles is:

A) \[\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{4{{p}_{1}}{{p}_{2}}}{{{x}^{4}}}\]            

B) \[\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{3{{p}_{1}}{{p}_{2}}}{{{x}^{3}}}\]

C) \[\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{6{{p}_{1}}{{p}_{2}}}{{{x}^{4}}}\]

D)        \[\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{8{{p}_{1}}{{p}_{2}}}{{{x}^{4}}}\]

Correct Answer: C

Solution :

[c]  Force of interaction \[F=\frac{1}{4\pi {{\in }_{0}}}.\frac{6{{p}_{1}}{{p}_{2}}}{{{x}^{4}}}\]