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Multiple choice torque on a dipole in a uniform electric field electric dipole electric charges and fields electrostatics physics

An electric dipole of dipole moment $\vec { P } $ is placed parallel to the uniform electric field of intensity $\vec { E }$. On rotating it through ${180}^{o}$, the amount of work done is ________ .

  1. $2PE$

  2. Zero
  3. $PE$
  4. $-2PE$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Work done by external agent in rotating the dipole 
$W=PE\left[ \cos { { \theta  } _{ 1 } } -\cos { { \theta  } _{ 2 } }  \right] $

Consider the initial angle to be
${ \theta  } _{ 1 }=0$ 

and the final angle will be
 ${ \theta  } _{ 2 }={ 180 }^{ o }$
So,$\Rightarrow$ $W=PE[cos\ 0^o-cos\ 180^o]=2PE$

Multiple choice torque on a dipole in a uniform electric field electric dipole electric charges and fields electrostatics physics

An electric dipole kept in a uniform electric field experiences :

  1. Force and a torque

  2. A force, but no torque

  3. A torque but no force

  4. Neither a force nor a torque
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

In a uniform electric field, both the point charges comprising the dipole will experience force, equal in magnitude and opposite in direction.
Though the net force will always be zero, the torque will be in same direction for both the charges. Hence torque will not be zero.

Multiple choice torque on a dipole in a uniform electric field electric dipole electric charges and fields electrostatics physics

When an electric dipole $\vec p$ is kept in a uniform electric field $\vec E$ then for what of a value of the angle between $\vec p$ and $\vec E$, torque will be maximum:

  1. ${90^o}$
  2. ${0^o}$
  3. ${180^o}$
  4. ${45^o}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$\overline { P } \times \overline { E } $

$=\overline { P } \overline { E } \sin{ 90 }^{ 0 }$
for maximum $\overline { P } \overline { E } $ then $\theta $ will be ${ 90 }^{ 0 }$.

Multiple choice torque on a dipole in a uniform electric field electric dipole electric charges and fields electrostatics physics

What will be the magnitude of torque on an electric dipole having dipole moment of $4\times { 10 }^{ -9 }cm$ placed in a uniform electric field of intensity of $5\times { 10 }^{ 4 \,\,}N { C }^{ -1 }$ making an angle ${180}^{o}$ with the field.

  1. ${ 10 }^{ -4 }N-m$
  2. $2\times { 10 }^{ -4 }N-m$
  3. $0$ (zero)
  4. ${ 10 }^{ -6 }N-m$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$\overrightarrow { \tau  } =\overrightarrow { p } \times \overrightarrow { E } $

$\overrightarrow{\tau} \longrightarrow$torque
$[\theta \longrightarrow$angle of the dipole moment$(p)$ with the field$(E)]$
$\therefore |\tau |=pE\sin { \theta  } =pE\sin { 180° } =0$

Multiple choice torque on a dipole in a uniform electric field electric dipole electric charges and fields electrostatics physics

An electric dipole  of dipole moment $\vec {p}$ is placed in uniform electric field $\vec {E}$, with $\vec {p}$ parallel to $\vec {E}$ . It is then rotated by an angle of $\theta$. The work done is

  1. $pE\ \sin \theta$
  2. $pE\ \cos \theta$
  3. $pE\ (1-\cos \theta)$
  4. $pE\ (1-\sin \theta)$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Work done in rotating a dipole in a uniform field is W = integral of tau d(theta) from 0 to theta, which equals pE(1 - cos(theta)).

Multiple choice torque on a dipole in a uniform electric field electric dipole electric charges and fields electrostatics physics

A dipole of $2 \mu C$ charges each other consists of the positive charge at the point $P(1, -1)$ and the m=negative charge is placed at the point $Q(-1,1)$ . The work done in displacing a charge of $ + 1 \mu C$ from point $A (-3,-3) $ to $B(4,4) $ is :

  1. $1.6 \times 10^{-19} J $
  2. $ 6.98 \times 10^{-3} J $

  3. Zero
  4. $4.8 eV $
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Since origin is the central point of the dipole, so electric potential on point ${P _1}\left( { - 3,3} \right)$

${V _1} = \dfrac{{k \times P\cos \theta }}{{{r^2}}}$

${V _1} = \dfrac{{9 \times {{10}^9} \times 2\sqrt 2  \times 2 \times {{10}^{ - 6}}}}{{{{\left( {3\sqrt 2 } \right)}^2}}} \times \dfrac{{\sqrt 2 }}{{\left( {3\sqrt 2 } \right)}}$

Similarly electric potential at point ${P _2}\left( {4,\;4} \right)$

${V _2} = \dfrac{{k \times P\cos \theta }}{{{r^2}}}$

${V _2} = \dfrac{{9 \times {{10}^9} \times 2\sqrt 2  \times 2 \times {{10}^{ - 6}}}}{{{{\left( {4\sqrt 2 } \right)}^2}}} \times \dfrac{{\sqrt 2 }}{{\left( {4\sqrt 2 } \right)}}$

Change in potential

$\Delta V = {V _1} - {V _2}$

$\Delta V = 9 \times {10^9} \times 2\sqrt 2  \times 2 \times {10^{ - 6}}\left( {\dfrac{1}{{18 \times 3}} - \dfrac{1}{{4 \times 32}}} \right)$

$\Delta V = 36\sqrt 2  \times {10^3}\left( {18.52 \times {{10}^{ - 3}} - 7.81 \times {{10}^{ - 3}}} \right)$

$\Delta V = 6.98 \times {10^3}{\rm{V}}$

Since potential at point ${P _1}$ is higher than potential at point ${P _2}$. The charge will move automatically from point ${P _1}$ to point ${P _2}$ under the effect of electric field of the dipole.

Now work done

$W = 6.98 \times {10^3} \times 1 \times {10^{ - 6}}$

$W = 6.98 \times {10^{ - 3}}{\rm{J}}$

Multiple choice torque on a dipole in a uniform electric field electric dipole electric charges and fields electrostatics physics

An electric dipole of moment 'p' is placed in an electric field of intensity 'E'. The dipole acquires a position such that the axis of the dipole makes an angle $\theta $ with the direction of the field. Assuming that the potential energy of the dipole to be zero when=${ 90 }^{ 0 }$, the torque and the potential energy of the dipole will respectively be

  1. $p E \sin { \theta } , pE\cos { \theta } $
  2. $p E \sin { \theta } ,-2p E\cos { \theta } $
  3. $p E \sin { \theta } ,2p E\cos { \theta } $
  4. $p E \cos { \theta } ,-p E\cos { \theta } $
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
An electric dipole of moment $=P$
electric field of intensity $=E$
the dipole acquire a position angle $=\theta$
dipole to be zero when $={ 90 }^{ 0 }$
torque and the potential energy of the dipole will respectively 
potential energy $U=PE\sin\theta $ in this situation.
$SIn$ component is benefited for that, perpendicularity and dipole is hence, $PEcos\theta $
Multiple choice torque on a dipole in a uniform electric field electric dipole electric charges and fields electrostatics physics

An electric dipole is placed in an electric field of a point charge then...........

  1. Force is always zero.

  2. Torque is always zero.

  3. Force is may be zero.

  4. Torque may be zero.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

A dipole in a point charge field experiences a torque that is zero only when the dipole axis is aligned with the radial line from the point charge. Thus, it is not always zero, but may be zero.

Multiple choice torque on a dipole in a uniform electric field electric dipole electric charges and fields electrostatics physics

Four equal positive charges each of magnitude $q$ are placed at the respective vertices of a square of side length $l$. A point charge $Q$ is placed at the centre of the square. Then

  1. $Q$ must not be in equilibrium
  2. $Q$ must be in stable equilibrium
  3. $Q$ must be in neutral equilibrium
  4. $Q$ must be in unstable equilibrium
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The four charges create a symmetric field. A charge Q at the center is in equilibrium. If displaced, the restoring force pushes it back toward the center, indicating stable equilibrium.