question_answer

Three identical dipoles are arranged as shown below. What will be the net electric field at \[P\left( k=\frac{1}{4\pi {{\varepsilon }_{0}}} \right)\]

A) \[\frac{k.p}{{{x}^{3}}}\]                                

B) \[\frac{2kp}{{{x}^{3}}}\]  

C) Zero                             

D) \[\frac{\sqrt{2}kp}{{{x}^{3}}}\]

Correct Answer: C

Solution :

Point P lies at equatorial positions of dipoles 1and 2 and axial position of dipole 3. Hence field at P due to dipole 1, \[{{E}_{1}}=\frac{k.p}{{{x}^{3}}}\,\,(towards\,\,left)\] due to dipole 2, \[{{E}_{2}}=\frac{k.p}{{{x}^{2}}}\,\,(towards\,\,left)\] due to dipole 3, \[{{E}_{3}}=\frac{k.(2p)}{{{x}^{3}}}\,\,(towards\,\,right)\] So net field at P will be zero.