question_answer

An electric dipole has the magnitude of its charge as q and its dipole moment is p. It is placed in a uniform electric field E. If its dipole moment is along the direction of the field, the force on it and its potential energy are respectively:                                                                                                                                      

A) 2qE and minimum   

B) qE and pE                   

C) zero and minimum 

D) qE and maximum

Correct Answer: C

Solution :

An electric dipole is an arrangement of two equal and opposite charges placed at a distance 2L The dipole is placed in electric field as such its dipole moment is in direction of electric field as shown in figure Now force on the charge q is \[{{F}_{2}}=qE\] along the direction of E and force on charge \[-q\]is\[{{F}_{1}}=-qE\] in the direction opposite to E. Since forces on the dipole are equal and opposite, so net force on the electric dipole is zero. Now potential energy of the dipole. \[U=-pE\cos \theta \] where\[\theta \]is the angle between direction of electric field and direction of dipole moment. \[\therefore \]                          \[\theta ={{0}^{o}}\] Hence, \[U=-pE\cos {{0}^{o}}=-pE\] (minimum)