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 an 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. \[\therefore \] \[\theta =0{}^\circ \] Hence, \[U=-pE\text{ }cos\text{ }0{}^\circ =-pE\] (minimum)