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  • If a magnetic dipole of dipole moment M is rotated through an angle <img alt="45^{\circ}" src="https://entrancecorner.oncodecogs.com/gif.latex?45%5E%7B%5Ccirc%7D"

If a magnetic dipole of dipole moment M is rotated through an angle 45^{\circ} with respect to the erection of the field H, then the work done is

Option: 1

MH\, \frac{\sqrt{2}+1} {\sqrt{2}}


Option: 2

MH\, \frac{\sqrt{2}-1}{\sqrt{2}}


Option: 3

MH\,\, \frac{1-\sqrt{2}}{\sqrt{2}}


Option: 4

MH \frac{\sqrt{2}}{\sqrt{2}-1}


Answers (1)

best_answer

The total work done

W =\int_0^\theta M H \sin \theta \, d \theta \\

     =\int_0^{\pi / 4} M H \sin \theta \, d \theta \\

 =M H[-\cos \theta]_0^{\pi / 4} \\

 =M H\left[-\frac{1}{\sqrt{2}}+1\right] \\

 =M H \frac{(\sqrt{2}-1)}{\sqrt{2}}

 

 

Posted by

Irshad Anwar

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