Tag: potential energy of a dipole in external field

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Questions Related to potential energy of a dipole in external field

Multiple choice physics electric charges and fields potential energy of a dipole in external field potential due to electric dipole electric dipole

An electric dipole consists of two opposite charges each of magnitude $2\mu C$ separated by a distance $1cm$. The dipole is placed in an external field of $10^3N/C$. The maximum torque on the dipole is

  1. $1\times 10^{-5}N-m$

  2. $2\times 10^{-5}N-m$

  3. $0.5\times 10^{-5}N-m$

  4. $Zero$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Torque tau = pE sin(theta). Max torque occurs at theta = 90 degrees, so tau_max = pE. p = q * d = (2*10^-6 C) * (0.01 m) = 2*10^-8 C-m. E = 10^3 N/C. tau_max = (2*10^-8) * (10^3) = 2*10^-5 N-m.

Multiple choice physics electric charges and fields potential energy of a dipole in external field potential due to electric dipole electric dipole

The relation connecting the energy U and distance r between dipole and induced dipole is :

  1. $U\propto r$

  2. $U\propto r^{2}$

  3. $U\propto r^{-6}$

  4. $U\propto r^{6}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The potential energy for the dipole-dipole interaction is given by $\displaystyle U=-\dfrac{2p _1^2p _2^2}{3(4\pi\epsilon _0)^2k _BT r^6}$
thus, $U \propto r^{-6}$

Multiple choice physics electric charges and fields potential energy of a dipole in external field potential due to electric dipole electric dipole

Carbon tetrachloride has zero dipole moment because of ________.

  1. planar structure

  2. Smaller size of C and Cl atoms

  3. regular tetrahedral structure

  4. none of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Carbon tetrachloride molecule has zero dipole moment even though C and Cl have different electronegativities and each of the C - Cl bond is polar and has some dipole moment. This is because the individual dipole moments cancel out because of the symmetrical tetrahedral shape of the molecule.



Multiple choice physics electric charges and fields potential energy of a dipole in external field potential due to electric dipole electric dipole

An electric dipole moment $ \overrightarrow { P }  $ is lying a uniform electric field $ \overrightarrow { E }  $ .The work done in rotation the dipole by $ 37^o $

  1. $ \dfrac {2}{5} PE $

  2. $ - \dfrac {2}{5} PE $

  3. $ \dfrac {PE}{5} $

  4. $ \dfrac {3}{5} PE $
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Work done W = pE(cos(theta1) - cos(theta2)). Assuming rotation from 0 to 37 degrees, W = pE(cos(0) - cos(37)) = pE(1 - 4/5) = pE/5.

Multiple choice physics electric charges and fields potential energy of a dipole in external field potential due to electric dipole electric dipole

An electric dipole is placed in an electric field generated by a point charge then

  1. Then net electric force on the dipole must be zero

  2. The net electric force on the dipole may be zero

  3. The torque on the dipole due to the field may be zero

  4. Both (2) and (3)
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

In a non-uniform field (like that of a point charge), the net force on a dipole is generally non-zero. However, the torque can be zero if the dipole is aligned with the radial field line.

Multiple choice physics electric charges and fields potential energy of a dipole in external field potential due to electric dipole electric dipole

An electric dipole when placed in a uniform electric field $E$ will have a minimum potential energy if the dipole moment makes the following angle with $E$

  1. $\pi$

  2. $\pi /2$

  3. zero

  4. $3\pi /2$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

${ U } _{ p }=-p\bullet E=-pE\cos { \theta  } $
${ \left( { U } _{ p } \right)  } _{ minimum }=-pE$
$\theta ={ 0 }^{ o }$${ U } _{ p }=-p\bullet E=-pE\cos { \theta  } $
${ \left( { U } _{ p } \right)  } _{ minimum }=-pE$
$\theta ={ 0 }^{ o }$

Multiple choice physics electric charges and fields potential energy of a dipole in external field potential due to electric dipole electric dipole

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:

  1. q. E and p. E

  2. zero and minimum

  3. q. E and maximum

  4. 2q. E and minimum
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$F = p\dfrac{dE} {dr} = 0 \left ( \because E = constant \right )$
$u = -\overrightarrow{p} \overrightarrow{E} = -PE \left ( minimum \right )$

Multiple choice physics electric charges and fields potential energy of a dipole in external field potential due to electric dipole electric dipole

Intensity of an electric field (E) depends on distance $r$. In case of dipole, it is related as :

  1. $ E \propto \cfrac{1}{r}$

  2. $ E \propto \cfrac{1}{r^{2}}$

  3. $ E \propto \cfrac{1}{r^{3}}$

  4. $ E \propto \cfrac{1}{r^{4}}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Intensity of electric field due to a Dipole
$ E = \cfrac{p}{4\pi \varepsilon _{0}r^{3}} \sqrt{3cos^{2 }\theta+1}\Rightarrow E \propto \cfrac{1}{r^{3}}$

So, we can just dimensionally tell that Electric field will be inversely proportional to third power of $r$.

Multiple choice physics electric charges and fields potential energy of a dipole in external field potential due to electric dipole electric dipole

A point charge $Q$ lies on the perpendicular bisector of an electric dipole of dipole $p$. If the distance of $Q$ from the dipole is $r$ (much larger than the size of the dipole).then the electric field at $\theta$ is proportional to :

  1. $P^{2}$ and $r^{-3}$

  2. $P$ and $r^{-2}$

  3. $P^{-1}$ and $r^{-2}$

  4. $P$ and $r^{-3}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

$\begin{array}{l} As\, \, we\, \, have, \ if\, \, r>1 \ { P _{ axi } }=\frac { 1 }{ { 4\pi { E _{ 0 } } } } \frac { { 2P } }{ { { r^{ 3 } } } }  \ { V _{ axi } }=\frac { 1 }{ { 4\pi { E _{ 0 } } } } \frac { P }{ { { r^{ 2 } } } }  \ Where\, \, in, \ Angle\, \, between\, \, { P _{ axi } }\, \, and\, \, P\, \, is\, 0. \ { E _{ equatorial } }=\frac { { kp } }{ { { r^{ 3 } } } }  \ i.e\, \, \, E\propto p \ and\, \, P\propto { r^{ -3 } } \end{array}$

Hence, Option $D$ is correct answer.