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. $40 \pi\, rad \,s ^{-2}$
• B. $20 \pi\, rad \,s ^{-2}$
• C. $5 \pi\, rad \,s ^{-2}$
• D. $15 \pi \,rad \,s ^{-2}$

Answer 1

Answer: (A)

Due to torque of magnetic field, ring will rotate about vertical diameter.
$\tau=I \alpha \Rightarrow M B=I \alpha$
$\Rightarrow i \pi r^{2} B=\frac{1}{2} m r^{2} \alpha$
$\Rightarrow \alpha=\frac{2 i B \pi}{m}$
$=\frac{2 \times 4 \times 10 \pi}{2}=40 \pi rads ^{-2}$