Question

Work done in rotating a magnetic dipole from 90 to 180

Answer 1

First of all

Torque-rxF,

here force F is simply equal to q.E (since this

E is taken as uniform). q is the charge of

dipole and r is the length of the dipole.

if theta is the angle between the vectors r

and F

Torque-rqE sin(theta), now this r.q is

nothing but the dipole moment p.

Torque-pE sin(theta)

suppose one rotates the dipole through an

angle d(theta) in anticlockwise direction.

then the work done

dw-pE sin(theta). d(theta)

integrating the expression between theta= 0

and theta 180 degree

the work done

W Integ [pE sin(theta). d(theta) ] between

limits of angle theta -0 and theta 180

degrees.

W- pE Integ [sin(theta). d(theta) ]1

between limits of angle theta 0 and theta

180 degrees.

W- pE[-cos (theta)] between limits of angle

theta 0 and theta 180 degrees.

W-2.r.q.E and is positive as the external

agent is doing the work.

hope it helped you out with the question

thanks

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