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 20.140. The initial angular acceleration of the ring will be

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 20.140. The initial angular acceleration of the ring will be (A) 40 π rad s -2 (B) 20 π rad s -2 (C) 5 π rad s -2 (D) 15 π rad s -2

Tardigrade Admin · Accepted Answer

Due to torque of magnetic field, ring will rotate about vertical diameter. τ=I α ⇒ M B=I α ⇒ i π r2 B=(1/2) m r2 α ⇒ α=(2 i B π/m) =(2 × 4 × 10 π/2)=40 π rads -2

Q. A conducting ring of mass $2 k g$ 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 $20.140$ . The initial angular acceleration of the ring will be

$40 π r a d s^{- 2}$

$20 π r a d s^{- 2}$

$5 π r a d s^{- 2}$

$15 π r a d s^{- 2}$

Due to torque of magnetic field, ring will rotate about vertical diameter.
$τ = I α \Rightarrow MB = I α$
$\Rightarrow iπ r^{2} B = \frac{1}{2} m r^{2} α$
$\Rightarrow α = \frac{2 i B π}{m}$
$= \frac{2 \times 4 \times 10 π}{2} = 40 π r a d s^{- 2}$

Q. A conducting ring of mass 2kg and radius 0.5m is placed on a smooth horizontal plane. The ring carries a current of i=4A. A horizontal magnetic field B=10T is switched on at time t=0 as shown in figure 20.140. The initial angular acceleration of the ring will be

40πrads−2

20πrads−2

5πrads−2

15πrads−2