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: [AIPMT (S) 2004]

A) \[2qE\] and minimum.

B) \[qE\] and \[pE\]

C) zero and minimum

D) \[qE\] and maximum

Correct Answer: C

Solution :

[c] An electric dipole is an arrangement of two equal and opposite charges placed at a distance 2 L 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)