Looking for classes? Ksquare Career Institute, Bengaluru →
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
q. E and p. E
B
zero and minimum
C
q. E and maximum
D
2q. E and minimum
Detailed Solution
In a uniform field, the charge $+q$ experiences force $qE$ along the field and $-q$ experiences force $qE$ opposite to the field. The net force is zero.
(In general $F = p\dfrac{dE}{dr}$, which is zero because E is constant.)
Potential energy of a dipole: $U = -\vec{p}\cdot\vec{E} = -pE\cos\theta$
When $\vec{p}$ is along $\vec{E}$, $\theta = 0^\circ$ and $U = -pE$, which is the minimum possible value (stable equilibrium).
So the force is zero and the potential energy is minimum.
(In general $F = p\dfrac{dE}{dr}$, which is zero because E is constant.)
Potential energy of a dipole: $U = -\vec{p}\cdot\vec{E} = -pE\cos\theta$
When $\vec{p}$ is along $\vec{E}$, $\theta = 0^\circ$ and $U = -pE$, which is the minimum possible value (stable equilibrium).
So the force is zero and the potential energy is minimum.