Physics

Electrostatics

303 Questions

Electrostatics deals with electric charges, fields, and potentials at rest. It is a crucial topic for physics sections in engineering and civil services competitive examinations. Review these questions to build a strong understanding of Coulomb law, electric dipoles, Gauss law, and electric flux.

Electric field and potentialElectric dipole momentGauss Law applicationsCoulomb force calculationsCharge distribution on spheresEquipotential surfaces

Electrostatics Questions

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

An electric dipole, made up of positive and negative charges, each of $1\mu C$ and placed at a distance $2\ cm$ apart. If the dipole is placed in an electric field of $10^{5} N/C$ then the maximum torque which the field can exert on the dipole, if it is turned from a position $\theta = 0^{\circ}$ to $\theta = 180^{\circ}$ is, is

  1. $2\times 10^{-3} N-m$
  2. $3\times 10^{-3} N-m$
  3. $4\times 10^{-3} N-m$
  4. $2.8\times 10^{-3} N-m$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Maximum torque is tau = pE. Given q = 10^-6 C, d = 0.02 m, E = 10^5 N/C. p = qd = 2 * 10^-8 C-m. tau = (2 * 10^-8) * 10^5 = 2 * 10^-3 N-m.

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

If a dipole of dipole moment $\displaystyle \vec { p } $ is placed in a uniform electric field $\displaystyle \vec { E } $, then torque acting on it is given by :

  1. $\displaystyle \vec {\tau } =\vec { p } .\vec { E } $
  2. $\displaystyle \vec { \tau } =\vec { p } \times \vec { E } $
  3. $\displaystyle \vec { \tau } =\vec { p } +\vec{ E } $
  4. $\displaystyle \vec { \tau } =\vec { p } -\vec { E } $
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Dipole moment of the dipole p and uniform Electric field $E$. we know that dipole moment $p = qa$ (where q is charge and a is the dipole length).And when a dipole of Dipole moment p is placed in a uniform Electric field E , the torque $\tau = Either  force \times \text{perpendicular  distance  between  the  two  forces }= qaE sin \theta$ or $\tau = pEsin \theta$ or $\tau = p \times E$

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

A dipole is placed parallel to the electric field. If W is the work done in rotating the dipole by 60, then work done in rotating it by 180 is

  1. 2 W

  2. 3 W

  3. 4 W
  4. ${\frac{W}{2}}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The work done in rotating a dipole from theta_1 to theta_2 is W = pE(cos(theta_1) - cos(theta_2)). For a rotation from 0 to 60 degrees, W = pE(1 - 0.5) = 0.5 pE. For a rotation from 0 to 180 degrees, W_total = pE(1 - (-1)) = 2 pE. Comparing the two results, 2 pE is exactly four times 0.5 pE, making the work 4 W.

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 generated by a point charge.

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

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

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

  4. The torque on the dipole due to the field may be zero.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

A and B cannot be true in any case. Because for the net force on a dipole to be zero, the field lines should be parallel to each other and the dipole must be placed perpendicular to the field. However, in case of point charge you cannot have parallel field lines. 
C: Not true again. Because in any orientation (except radial) the force on the positive and negative charge will form a couple and you will have torque.
D: True. If you place the dipole radial from the point object, then there will be no net torque. Since torque $=F\times R\;\sin{\theta}$. If it is radial, $\sin{\theta}=0$, so torque $=0$. 

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

State whether True or False :

In a uniform electric field, the dipole experiences no net force; but experiences a torque having a relation with $P$ and $E$ which is given by $\vec{P} \times \vec{E}$ where the parameters $P$ and $E$ have their usual meaning.

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
Torque ($\tau$)  = Force × distance seperating forces
$\tau = d \space  qE sin \theta$
Since dipole moment is given by $P = qd$
$\therefore \tau =PE sin \theta$ or
$\overrightarrow \tau = \overrightarrow P \times \overrightarrow E$. 
In a uniform electric field, we know that the dipole experiences no net force; but experiences a torque having a relation with P and E is given by $\overrightarrow \tau = \overrightarrow P \times \overrightarrow E$ where the parameters P and E have their usual meaning.
Multiple choice torque on a dipole in a uniform electric field electric dipole electric charges and fields electrostatics physics

The torque acting on a dipole of momentum $\vec { p } $ in an electric field $\vec { E } $:

  1. $\vec { p } \times \vec { E } $
  2. $\vec { p } .\vec { E } $

  3. zero
  4. $\vec { E } \times \vec { p } $
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Force acting on dipole due to electric field is given by,

$F=qE$
Torque on a dipole in an electric field is given by,
$T= F\times d = Fdsin\theta=qEdsin\theta$.     .....(i)
But dipole moment is given by,
$P=qd$    ....(ii)
By (i) and (ii) we get,
$\therefore$ $T= pEsin\theta=\overrightarrow{p}\times \overrightarrow{E}$

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

An electric dipole of moment $\vec { p } $ is placed normal to the lines of force of electric intensity $\vec { E } $, then work done in deflecting it through an angle of ${180}^{o}$ is:

  1. $pE$
  2. $+2pE$
  3. $-2pE$

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

Work done $W=pE(\cos\phi _1-\cos\phi _2)$

$\phi _1=90^\circ,\phi=180^\circ$
$W=pE(0-(-1))$
$W=pE$

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

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.