(a) Magnetic moment, `M=1.5J T^(-1)`
Magnetic field strength, `B=0.22T`
(i) Initial angle between the axis and the magnetic field `theta_(1)=0^(@)`
Final angle between the axis and the magnetic field `theta_(2)=90^(@)`
The work required to make the magnetic moment normal to the direction of magnetic
field is given as:
`W=-MB(cos theta_(2)-costheta_(1))`
`=-1.5xx0.22(cos 90^(@)-cos0^(@))`
`=-0.33(0-1)`
`=0.33 J`
(ii) Initial angle between the axis and the magnetic field, `theta_(1)=0^(@)`
Final angle between the axis and the magnetic field, `theta_(2)=180^(@)`
The work required to make the magnetic moment opposite to the direction of magnetic field is given as:
`W=-MB(costheta_(2)-costheta_(1))`
`=-1.5xx0.22(cos 180-cos0^(@))`
`= -0.33(-1-1)`
`=0.66J`
(b) For case i: `theta=tehta_(2)=90^(@)`
`therefore` Torque, `r=MB sin theta`
`=1.5xx0.22sin90^(@)`
=0.33J
For case ii: `theta=theta_(2)=180^(@)`
`therefore` Torque, `r=MB sin theta`
`=MB sin 180^(@)=0J`