Physics

Electrostatics

299 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

A dipole is placed in an electric field whose direction is fixed but its magnitude varies with distance. It is possible that the dipole experiences :

  1. no net force and no torque

  2. a net force but no torque

  3. a net force and a torque

  4. no net force but a torque
Reveal answer Fill a bubble to check yourself
B,C,D Correct answer
Explanation

Dipole means two charges $+q$ and $-q$ are placed at a certain distance.
There  three cases may be occured for electric field whose direction is fixed but magnitude varies with distance.
1) when forces on the two charges are in different direction and different magnitude, they will have a net force and a torque.
2) when forces on the two charges are in same direction but different magnitude, they will have a net force but no torque.
3) when forces on the two charges are in opposite direction but same magnitude, they will have no net force but a torque.

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 kept along an electric field E. The work done in rotating it from an equilibrium position by an angle $\theta$ is :

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

Electric field will produce a torque on the dipole.
Torque , $\displaystyle \tau=pE\sin\theta$
The work done in rotating it from an equilibrium position by an angle $\theta$ is $\displaystyle W=\int _0^{\theta}\tau d\theta=pE\int _0^{\theta}\sin\theta d\theta=-pE(\cos\theta-\cos0)=pE(1-\cos\theta)$

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

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

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

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.