Question

A non conducting ring of radius $r=10\text{cm}$ and mass $m=500\text{g}$ which has a total charge $Q=5\text{C}$ distributed uniformly on it. The ring is rotated about its axis with a uniform speed $v=0.2\pi \text{m/s}$ as shown. Find angular momentum of the ring using magnetic moment.

• A. $0.01\pi$
• B. $0.03\pi$
• C. $0.05\pi$
• D. $0.1\pi$

Answer 1

The correct option is A $0.01\pi$

Current in a non conducting rotating ring is given by $$i=\frac{Q\omega }{2\pi }$$And we know that, $\omega =\frac{v}{r}$

From the data given in the question,

$i=\frac{5\times 0.2\pi }{2\pi \left(0.1\right)}=5\text{A}$

Magnetic moment of the non conducting rotating ring is given by $$\mu =iA=i\left(\pi r^2\right)$$$\Rightarrow \mu =5\times \pi \times (0.1{)}^2=0.05\pi {\text{Am}}^2$

We know that, $\mu =\frac{Q}{2m}L$

$\Rightarrow L=\frac{\mu \times 2m}{Q}=\frac{0.05\pi \times 2\times 0.5}{5}=0.01\pi {\text{kgm}}^2/\text{s}$

Hence, option (c) is the correct answer.