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

A magnetic dipole is placed at right angles to the direction of lines of force of magnetic induction B. If it is rotated through an angle of $180^0$, then the work done is 

  1. 2 MB

  2. MB

  3. -2 MB

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

Work done in rotating a magnetic dipole is W = MB(cos(theta1) - cos(theta2)). Rotating from 90 degrees to 270 degrees (180 degree rotation) results in W = MB(cos(90) - cos(270)) = MB(0 - 0) = 0.

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 electri dipole experience linear displacement and  rotational motion in _____ electric field.

  1. uniform

  2. non-uniform

  3. none

  4. a&b both
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

In a uniform electric field, the net force on a dipole is zero, so it only experiences rotation. In a non-uniform field, the forces on the two charges are unequal, leading to both a net force (linear displacement) and a torque (rotational motion).

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