Question

A non conducting ring of radius $r=10\text{cm}$ and mass $m$ which has a total charge $Q=5\text{C}$ distributed uniformly on it. The ring is rotated about its axis with an angular speed $\omega =2\pi \text{rad/s}$ as shown. Find the equivalent electric current (in amperes) in the ring and also find the magnetic moment (in${\text{Am}}^2$) of the ring.

• A. $5;0.05\pi$
• B. $10;0.05\pi$
• C. $5;0.01\pi$
• D. $5;0.5\pi$

Answer 1

The correct option is A $5;0.05\pi$

Current in a non conducting rotating ring is given by $$i=\frac{Q\omega }{2\pi }$$From the data given in the question,

$i=\frac{5\times 2\pi }{2\pi }=5\text{A}$

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$

Hence, option (a) is the correct answer.