First slide

Magnetism

Question

A circular coil has moment of inertia 0.8 $k g m^{2}$ around any diameter and is carrying current to produce a magnetic moment of 20 $A m^{2}$ . The coil is kept initially in a vertical position and it can rotate freely around a horizontal diameter. When a uniform magnetic field of 4 T is applied along the vertical, it starts rotating around its horizontal diameter. The angular speed the coil acquires after rotating by $60 °$ will be:

Moderate

A

$10 \times 3^{1 / 4} {rads}^{- 1}$
B

$10 π {rads}^{- 1}$
C

$20 π {rads}^{- 1}$
D

$20 {rads}^{- 1}$

Solution

$A p p l y i n g c o n s e r v a t i o n o f e n e r g y :$
$\begin{array}{l} \frac{1}{2} I ω^{2} = MB \{\cos θ_{f} - \cos θ_{i}\} [θ_{i} = 90^{0}, a f t e r r o t a t i n g b y 60^{0}, θ_{f} = 30^{0}] \end{array}$
$\Rightarrow \frac{1}{2} \times 0.8 \times ω^{2} = 20 \times 4 (\frac{\sqrt{3}}{2})$
$\begin{array}{l} \Rightarrow ω = 10 \times 3^{1 / 4} r a d s^{- 1} \end{array}$

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