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

A electric dipole moment $\vec { p } =\left( 2.0\hat { i } +3.0\hat { j }  \right) \mu C.m$ is placed in a uniform electric field $\vec { E } =\left( 3.0\hat { i } +2.0\hat { k }  \right) \times { 10 }^{ 5 }N{ C }^{ -1 }$

  1. The torque that $\vec { E }$ exerts on $\vec { p }$ is $\left( 0.6\hat { i } -0.4\hat { j } -0.9\hat { k } \right) Nm$

  2. The potential energy of the dipole is $-0.6J$

  3. The potential energy of the dipole is $0.6J$

  4. If the dipole is free to rotate in the electric field, the maximum magnitude of potential energy of the dipole during the rotation is $1.3J$
Reveal answer Fill a bubble to check yourself
A,B,D Correct answer
Explanation

$\vec P = (2 \widehat i + 3 \widehat j) \mu cm$.
$\vec E = (0.3 \widehat i + 0.2 \widehat k) N \mu C^{-1}$
$\vec C = \vec P \times \vec E$
$=\begin{vmatrix}\widehat i & \widehat j & \widehat k\ 2 & 3 & 0\0.3  & 0 & 0.2\end{vmatrix}$
$= \widehat i (0.6) - \widehat (0.4) + \widehat k (-0.9)$
$= 0.6 \widehat i - 0.4 \widehat j - 0.9 \widehat k$
$U =- \vec P \cdot \vec E$
$=- (2 \widehat i + 3 \widehat j) \cdot (0.3 \widehat i + 0.2 \widehat k)$
$=- 0.6 J$
Consider,
the dipole rotated by 180$^o$.

The magnitude of dipole moment will not change only its direction will change.
$\therefore U=-\vec{P}.\vec{E}=|P||E|\ Sin\theta$
the max value of U is $|P||E|$
$=\sqrt{13} \times 10^{-6} \times \sqrt{13} \times 10^5
= 1.3 J.$
This is the maximum potential energy of the dipole.

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 of moment $P$ is placed in the position of stable equilibrium in uniform electric field of intensity $E$. It is rotated through an angle $\theta$ from the initial position. The potential energy of electric dipole in the position is

  1. $\mathrm { pE } \cos \theta$

  2. $\mathrm { pE } \sin \theta$

  3. $\mathrm { pE } ( 1 - \cos \theta )$

  4. $\mathrm {- pE } \cos \theta$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Stable equilibrium is at theta = 0. Potential energy U = -pE cos(theta). Rotating to angle theta gives U(theta) = -pE cos(theta). The change in potential energy relative to the stable position is U(theta) - U(0) = -pE cos(theta) - (-pE) = pE(1 - cos(theta)).

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

 A small dipole is placed is located at the center of an imaginary spherical Gaussian surface (radius R) with its dipole moment in +X-direction . Let $E _{max}$ & $E _{min}$  be maximum & maximum possible magnitude of field over the surface. 
Statement 1:   Number of points where E = $E _{max}$ is infinite.
Statement 2:    Number of points where E = $E _{min}$ is two.

  1. Both 1 and 2 are correct

  2. Both 1 and 2 are incorrect

  3. Only 1 is correct

  4. Only 2 is correct
Reveal answer Fill a bubble to check yourself
C Correct answer
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  } $
${ \left( { U } _{ p } \right)  } _{ minimum }=-pE$
$\theta ={ 0 }^{ o }$