Tag: torque on a dipole in a uniform electric field

Questions Related to torque on a dipole in a uniform electric field

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 :

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

  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

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Correct Option: B,C,D
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.

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 :

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

  1. PE(1 - cos $\theta$)

  2. PE(1 - sin $\theta$)

  3. PE cos $\theta$

  4. PE sin $\theta$

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Correct Option: A
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 $\displaystyle W=\int _0^{\theta}\tau d\theta=pE\int _0^{\theta}\sin\theta d\theta=-pE(\cos\theta-\cos0)=pE(1-\cos\theta)$

An electric dipole is kept in the surrounding of another dipole, it experiences

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

  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

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Correct Option: C

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.

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

  1. $10 ^ { - 4 } N - m$

  2. $0$ 

  3. $2\times 10^{ { -4 } }{ N }-{ m }$

  4. $10 ^ { -6 } N - m$

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Correct Option: B

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

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

  1. $2\times 10^{-3} N-m$

  2. $3\times 10^{-3} N-m$

  3. $4\times 10^{-3} N-m$

  4. $2.8\times 10^{-3} N-m$

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Correct Option: A

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 :

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

  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 } $

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Correct Option: B
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 $\tau = p \times E$

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

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

  1. 2 W

  2. 3 W

  3. 4 W

  4. ${\frac{W}{2}}$

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Correct Option: B

An electric dipole is placed in an electric field generated by a point charge.

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

  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.

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Correct Option: D
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 $=0$. 

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

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

  1. only torque

  2. force and torque

  3. only force

  4. neither force nor torque

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Correct Option: B
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.

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.

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

  1. True

  2. False

Show answer
Correct Option: A
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.