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Units And Measurement

Question
CBSEENPH11020737

A bar magnet having a magnetic moment of 2 x 104 JT-1 is free to rotate in a horizontal plane. A horizontal magnetic field B = 6 x 10-4 T exists in the space. The work  is done in taking the magnet slowly from a direction parallel to the field to a direction 60o from the field is

  • 0.6 J

  • 12 J

  • 6 J

  • 2 J

Solution

C.

6 J

The work done in rotating a magnetic dipole against the torque acting on it, when placed in a magnetic field is stored inside it in the form of potential energy. 
When magnetic dipole is rotated from initial position θ = θ1 to final position θ = θ2, then work done = MB (cos θ1 = cos θ2)
space equals space MB space open parentheses 1 minus 1 half close parentheses
space equals space fraction numerator 2 space straight x space 10 to the power of 4 space straight x space 6 space straight x space 10 to the power of negative 4 end exponent over denominator 2 end fraction space equals space 6 space straight J