Question

VID
The potential energy of a bar magnet of magnetic moment 8 A m2 placed in a uniform magnetic field of 2 T
at an angle of 120° is equal to
(1) -16 J
(2) 16 J
(4) -8 J
(3) 8J​

Answer 1

Answer:

8J

Explanation:

$\\\tt \tau = M \times B$

(cross product)

Where M= magnetic moment and B= magnetic field

And so PE will be given by:

$\\\tt \int\limits {\tau} \, d\theta = \int\limits {MB sin(\theta)} \, d\theta \\ =-MBcos(\theta)$

Using the given values now,

$\\\tt P.E = -8 \ Am^{-2} (2T) cos (120 ^{\circ}) \\ =- 8 \ Am^{-2} (2T) ( -\dfrac{1}{2} )\\= +8J$

Note that:  Tau is rotational equivalent of force so $\\\tt \tau.d\theta$ is rotational equivalent of F.dr which is work.

Answer 2

Required Answer :-

We know that

$\sf PE = -MB cos\theta$

M = 8

B = 2

cos theta = 120 = -1/2

$\sf PE = -8 \times 2 \times \dfrac{-1}{2}$

$\sf PE = -8 \times 2 \times \dfrac{1}{-2}$

$\sf PE = 4 \times 2 \times 1$

$\sf PE = 8 \; J$