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Consider an electric dipole comprising two charges +q and -q each with mass m , separated by a fixed distance d and initially at rest with its dipole moment pointing along i . A uniform electric field E j is turned on at time t = 0 and it is turned off at t = t_f , when the dipole moment makes an angle _f with i . Neglecting any sources of energy loss, correct option(s) is/are:

Options

  1. AThe center of mass of the dipole is deflected towards j in the presence of the field.
  2. BIf the magnitude of the final angular velocity _f = 2qE md , then _f = 6 .
  3. CIf _f = /3 , then the change in kinetic energy of the dipole is given by 2 3 , qEd .
  4. DFor _f = /4 , the dipole rotates around its center of mass with a constant angular velocity after t > t_f .

Correct answer

B. If the magnitude of the final angular velocity _f = 2qE md , then _f = 6 .

Step-by-step solution

The net force on the dipole in a uniform electric field is zero, as the forces on the two charges are equal and opposite ( qE j and -qE j ). Therefore, the center of mass remains at rest and is not deflected. Option (A) is incorrect. The moment of inertia of the dipole about its center of mass is I = m ( d 2 )^2 + m ( d 2 )^2 = md^2 2 . The torque on the dipole is = p E . The angle between the dipole moment p and the electric field E is 90^ - . The magnitude of the torque is = pE (90^ - ) = qdE . The work done by t

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