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Electrostatics question

2006 · Shift 0 · Q114
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Electrostatics question

2006 · Shift 0 · Q114

JEE MainPhysicsElectrostaticsMCQ+4 / −1
An electric dipole is placed at an angle of 30∘{30^ \circ }30∘ to a non-uniform electric field. The dipole will experience
  1. A
    a translation force only in the direction of the field
  2. B
    a translation force only in a direction normal to the direction of the field
  3. C
    a torque as well as a translational force
  4. D
    a torque only
View written solutionFree

Correct answer: C

  1. Forces on a dipole in an electric field

An electric dipole consists of charges +q+q+q and −q-q−q separated by a small distance.

  • In a uniform electric field, the forces on the two charges are equal and opposite, so the net force is zero.
  • However, if the dipole is inclined to the field, these forces form a couple and produce a torque.

So in a uniform field:

  • net force =0=0=0
  • torque =pEsin⁡θ=pE\sin\theta=pEsinθ
  1. Effect of a non-uniform electric field

In a non-uniform electric field, the magnitudes/directions of the electric field at the two charges are not exactly the same.

Hence the forces on +q+q+q and −q-q−q do not cancel completely.

Therefore, the dipole experiences:

  • a net translational force, and
  • since it is at an angle 30∘30^\circ30∘ to the field, also a torque.
  1. Torque on the dipole

The torque is

τ=pEsin⁡θ\tau = pE\sin\thetaτ=pEsinθ

Here θ=30∘\theta = 30^\circθ=30∘, so

τ=pEsin⁡30∘=pE2≠0\tau = pE\sin 30^\circ = \frac{pE}{2} \neq 0τ=pEsin30∘=2pE​=0

Thus torque definitely acts.

  1. Check the options
  • A: a translation force only in the direction of the field
    Incorrect, because torque also acts.

  • B: a translation force only in a direction normal to the direction of the field
    Incorrect, because torque also acts, and the force direction is not restricted like this in general.

  • C: a torque as well as a translational force
    Correct, because in a non-uniform field the dipole gets net force, and at 30∘30^\circ30∘ it also gets torque.

  • D: a torque only
    Incorrect, because a non-uniform field also produces a net translational force.

  1. Final answer

Therefore, the dipole will experience both torque and translational force.

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