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

Two electric dipoles of dipole moment $2 \space cm$ and $4 \space cm$ respectively are kept inside a cube of side $'a' \space m$. Total electric flux linked with the cube is (in SI units)

  1. $\dfrac{6}{\varepsilon _0}$
  2. $\dfrac{2}{\varepsilon _0}$
  3. $\dfrac{4}{\varepsilon _0}$

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

Since net charge $=0$

$\therefore \phi =0$
$\therefore$ option $D$ is correct answer.

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

An electric dipole of momentum $3 \times {10}^{-8}\ Cm$ is placed in an electric field of $6 \times {10}^{4}\ N/C$ with is axis making an angle of $30^o$ with the field . Find the torque acting on the dipole.

  1. $ (9 \times 10^{-5} )N-m$
  2. $ (9 \times 10^{-4} )N-m$
  3. $ (9 \times 10^{-3} )N-m$
  4. $ (90 \times 10^{-8} )N-m$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

We know that Torque $(\vec \tau) = \vec p \times \vec E$


$  \tau = pE\sin \theta$
$ = (3\times 10^{-8})\times ( 6\times 10^4) \sin30^0$
$ = (9 \times 10^{-4} )N-m$

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

A neutral water molecule $ (H _2 O) $ in its vapour state has an electric dipole moment of $ 2 \times 10^{-24} C-m. $ If the molecule is placed in an electric field of $ 2 \times 10^{4} NC^{ _1} $ , the maximum torque that the field can exert on it is nearly.

  1. $ 4 \times 10^{-20} N-m $
  2. $ 6 \times 10^{-20} N-m $
  3. $ 8 \times 10^{-20} N-m $
  4. $ 2 \times 10^{-18} N-m $
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$P = 2 \times 10^{-24}Cm$


$E = 2 \times 10^{4}NC$

$\tau = EP = 2 \times 10^{-24} \times 2 \times 10^{4} = 4 \times 10^{-20}Nm$

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 the work done in rotating it by $180$ is:

  1. $ 2W$
  2. $ 3W$
  3. $ 4W$
  4. $ W/2$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Work done in rotating dipole by $\theta \,$ angle from eqbm. ,$W = PE\left( {1 - \cos \theta } \right)$

$\begin{array}{l}W = PE\left( {1 - \cos 60^\circ } \right)\ = PE\left( {1 - \frac{1}{2}} \right) = \frac{{PE}}{2}\or\,\,\,PE = 2W\W' = PE\left( {1 - \cos 180^\circ } \right)\ = PE\left( {1 - \left( { - 1} \right)} \right)\ = 2PE = 2 \times 2W = 4W\end{array}$

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

Two charges of charge $-4\mu C$ and $+4\mu C$ are placed of the point $A(1, 0, 4)$ and $B(2, -1, 5)$ located in an electric field $E = 0.20\hat {i} V/ C-m$. Then, torque acting on the dipole will be

  1. $2.31\times 10^{-4} N/m$
  2. $7.98\times 10^{-4} C/m$
  3. $7.11\times 10^{-4} C/m$
  4. $7.04\times 10^{-4} C/m$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Torque is given by p x E. First, calculate the dipole moment vector p = q * d, where d is the vector from -q to +q. Then compute the cross product with the electric field E.

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

Dipole is placed parallel to the electric field. If W is the work done in rotating the dipole $60^0$, then work  done in rotating it by $180^0$ is

  1. 2 W

  2. 3 W

  3. 4 W

  4. W/2
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Work done in rotating an electric dipole from angle theta_1 to theta_2 in a uniform electric field is W = pE(cos(theta_1) - cos(theta_2)). Initially, it is parallel (theta = 0) and rotated by 60 degrees, so W = pE(cos(0) - cos(60)) = pE(1 - 0.5) = 0.5 pE. Rotating it by 180 degrees gives W_180 = pE(cos(0) - cos(180)) = pE(1 - (-1)) = 2 pE. Since 2 pE = 4 * (0.5 pE), the work done is 4 W.

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

In a certain region of space, electric field is along z-direction throughout. The magnitude of electric field is, however, not constant but increases uniformly along the positive z-direction, at the rate of $10^5 NC^{-1}$ per metre. What is the torque experienced by a system having a total dipole moment equal to $10^{-7}$ C-m in the negative z-direction?

  1. 2 N-m

  2. 3 N-m

  3. 4 N-m

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

$\tau =\vec P\times \vec E = PE \sin\theta $
Since, $ \theta = 180^o \rightarrow \tau =0 $

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

The work done in rotating a dipole through ${ 180 }^{ \circ  }$ from electric field direction is :

  1. $pE$
  2. $2pE$
  3. $\cfrac { pE }{ 2 } $
  4. $Zero$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Work done due to dipole $=W=-pE\cos\theta$ where $p=$ dipole moment, $E=$ electric field
Here, $W=W _{(180)}-W _{(0)}=(-pE\cos180)-(-pE\cos0)=pE+pE=2pE$
Ans: (B)

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

An electric dipole consists of two opposite charges each of magnitude $ 1.0 \mu C $ separated by a distance of 2.0 cm. the diople is placed in an external electric field of $ 1.0 \times  10^5 N/C $ the maximum torque on the dipole is:

  1. $ 0.2 \times 10^{-3} N-m $
  2. $ 1.0 \times 10^{-3} N-m $
  3. $ 2.0 \times 10^{-3} N-m $
  4. $ 4.0 \times 10^{-3} N-m $
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Maximum torque is given by tau = pE, where p = q * d. Here, p = (1.0 * 10^-6 C) * (0.02 m) = 2.0 * 10^-8 C-m. Then, tau = (2.0 * 10^-8) * (1.0 * 10^5) = 2.0 * 10^-3 N-m.

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

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  $5 \times 10 ^ { 4 } { NC } ^ { - 1 }$  making an angle  $180 ^ { \circ }$  with the field.

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

Torque is given by tau = pE sin(theta). When the dipole is at 180 degrees to the field, sin(180) = 0, resulting in zero torque.