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Electric Charges and Fields
Dipole in a Uniform Electric Field
2 questions from 2 papers, each with its answer.
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Appears in
Concepts tested
- Force and potential energy of a dipole
- Torque on a dipole
All Questions
2004 AIPMT 1 question
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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 :-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.
2001 AIPMT 1 question
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A dipole of moment $\vec{p}$ is placed in uniform electric field $\vec{E}$ then torque acting on it is given by : -The two charges of the dipole experience equal and opposite forces qE, which form a couple.
Torque magnitude $= qE \times 2a\sin\theta = pE\sin\theta$, directed perpendicular to both $\vec{p}$ and $\vec{E}$.
In vector form: $\vec{\tau} = \vec{p} \times \vec{E}$
(The dot product $-\vec{p}\cdot\vec{E}$ gives the potential energy, which is a scalar.)
