First slide

Applications involving charged particles moving in a magnetic field

Question

A conducting ring of mass 2 kg and radius 0.5 m is placed on a smooth horizontal plane. The ring carries a current of $i = 4 A$ . A horizontal magnetic field $B = 10 T$ is switched on at time $t = 0$ as shown in figure. The initial angular acceleration of the ring will be

Moderate

A

${40π rad s}^{-2}$
B

${20π rad s}^{-2}$
C

${5π rad s}^{-2}$
D

$15 π {rad s}^{-2}$

Solution

Due to torque of magnetic field, ring will rotate about vertical diameter.
$\begin{array}{l} τ = I α \Rightarrow M B \sin 90^{o} = I α \\ \Rightarrow i π r^{2} B = \frac{1}{2} m r^{2} α \\ \Rightarrow α = \frac{2 i B π}{m} = \frac{2 \times 4 \times 10 π}{2} = 40 π rad s^{- 2} . \end{array}$

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