question_answer

Two point dipoles of dipole moment \[\overset{\to }{\mathop{{{\operatorname{P}}_{1}}}}\,\] and \[\overset{\to }{\mathop{{{\operatorname{P}}_{2}}}}\,\] are at a distance \[x\] from each other and \[\overset{\to }{\mathop{{{\operatorname{P}}_{2}}}}\,||\overset{\to }{\mathop{{{\operatorname{P}}_{2}}}}\,\] The force between the dipoles is:                          [JEE ONLINE 09-04-2013]

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

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

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

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

Correct Answer: B

Solution :

[b]

Both the charges of each dipole will interact with both the charges of to the dipole with an electrostatic force and then by vector sum, we can find the net force on the dipole.

\[{{F}_{net}}=\frac{1}{4\pi {{\varepsilon }_{0}}}\,\frac{3{{p}_{1}}{{p}_{2}}}{{{X}^{4}}}\]