A magnet of magnetic dipole moment 5.0 `Am^(2)` is lying in a uniform magnetic field of `7 xx 10^(-4) T` such that its dipole moment vector makes an angle of 30° with the field. The work done in increasing this angle from 30° to 45° ls about ......... J.

Options

A. `5.56 xx 10^(-4)`
B. `24.74 xx 10^(-4)`
C. `30.3 xx 10^(-4)`
D. `5.50 xx 10^(-3)`

Answer

A

Explanation

`W = U_(2) - U_(1)`
`= - mB cos theta _(2) - (- m B cos theta )`
`= - mB ( cos theta_(2) - cos theta_(1) )`
`=-5 xx 7 xx 10^(-4) ( cos 45^(@) - cos 30^(@) )`
`= - 35 xx 10(-4) ((1)/(sqrt(2)) -(sqrt(3) ) /( 2)) `
`= - 35 xx 10^(-4) (-0.1588) = 5.558 xx 10^(-4)`
`therefore W ~~ 5.56 xx 10^(-4)` J