Tag: electric charges and fields

Quizzes (7) Questions (175)

Questions Related to electric charges and fields

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 is kept in the surrounding of another dipole, it experiences

  1. a force and a torque

  2. a force but not a torque

  3. a force but not necessarily a torque

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

The electric field produced by a dipole is non-uniform. Therefore, another dipole placed in this field will experience a non-zero net force and a torque, depending on its orientation and position.

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.

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

An electric dipole is placed in non-uniform electric field, then it experiences

  1. only torque

  2. force and torque

  3. only force

  4. neither force nor torque
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Given an electric dipole placed in a non-uniform electric field. An electric dipole always experiences a torque when placed in uniform as well as non-uniform electric field. But in non-uniform electric field, dipole will also experience net force of attraction. So the electric dipole in non-uniform electric field experiences both torque and force.

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,
$\therefore$ $T= pEsin\theta=\overrightarrow{p}\times \overrightarrow{E}$