1. Tardigrade
  2. Question
  3. Physics
  4. Consider the following statements about electric dipole and select the correct ones. S1: Electric dipole moment vector vec p is directed from the negative charge to the positive charge. S2: The electric field of a dipole at a point with position vector vec r depends on | vec r | as well as the angle between vec r and vec p . S3: The electric dipole potential falls off as (1/r2) and not as (1/r). S4: In a uniform electric field, the electric dipole experiences no net forces but a torque vecτ= vec p × vec E .

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Q. Consider the following statements about electric dipole and select the correct ones.
$S_1$: Electric dipole moment vector $\vec{ p }$ is directed from the negative charge to the positive charge.
$S_2$ : The electric field of a dipole at a point with position vector $\vec{ r }$ depends on $|\vec{ r }|$ as well as the angle between $\vec{ r }$ and $\vec{ p }$.
$S_3$ : The electric dipole potential falls off as $\frac{1}{r^{2}}$ and not as $\frac{1}{r}$.
$S_4$: In a uniform electric field, the electric dipole experiences no net forces but a torque $\vec{\tau}=\vec{ p } \times \vec{ E }$.

AMUAMU 2010Electrostatic Potential and Capacitance

Solution:

(i) An electric dipole is a pair of equal and opposite charges $q$ and $-q$ separated by same distance $2\, L$
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(ii) The electric field due to a dipole at a point $P$ is
$E=\frac{p}{4 \pi \varepsilon_{0}} \frac{\sqrt{3 \cos ^{2} \theta+1}}{r^{3}} (r \gg a)$
(iii) The electric potential due to dipole in its general position is given by
$V=\frac{k \cdot p \cos \theta}{r^{2}}$
$V \propto \frac{1}{r^{2}}$
So, the electric dipole potential falls off as
$\frac{1}{r^{2}}$ and not as $\frac{1}{r}$.
(iv) In a uniform electric field, the electric dipole experiences no net force but a torque
$\tau=\vec{ p } \times \vec{ E }$