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Moving Charges And Magnetism

Question
CBSEENPH12039887

An electric dipole of moment p is placed in an electric field of intensity E. The dipole acquires a position such that the axis of the dipole makes an angle θ with the direction of the field. Assuming that the potential energy of the dipole to be zero when θ =90o, the torque and the potential energy of the dipole will respectively be

  • pE sin θ, pE cos θ

  • pE sin θ,-2pE cos θ

  • pE sin θ, 2 pE cos θ

  • pE cos θ,-pE sin θ

Solution

A.

pE sin θ, pE cos θ

Here
Torque =pE sin θ


potential space energy space of space the space dipole
straight U equals negative integral straight tau space dθ

equals negative integral subscript straight pi divided by 2 end subscript superscript 0 space pE space sin space straight theta space dθ space equals space pE left square bracket cosθ minus 0 right square bracket
equals negative pE space cosθ