Tag: torque on a dipole in a uniform electric field

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

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

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.