A current carrying loop is placed in a uniform magnetic field in four different orientations , I,ii,iii & iv arrange them in the decreasing order of potential Energy`

Options

A. `I gt III gt II gt IV`
B. `I gt II gt III gt IV`
C. `I gt IV gt II gt III`
D. `III gt IV gt I gt II`

Answer

C

Explanation

`U =-vec(M) . vec(B) = -MB cos theta`
I. `U_(1) = -MB cos (180^(@)) = MB`
II. `U_(2) = -MB cos (90^(@)) = 0`
III. `U_(3) = -MB cos theta, theta lt 90^(@), U_(3)` is `-ve`
IV. `U_(4) = -MB cos theta, theta gt 90^(@), U_(4)` is `+ve`, `U_(4) lt MB`
`U_(1) gt U_(4) gt U_(2) gt U_(3)`
`I gt II gt III`