Question

Consider a quarter circular conducting ring of large radius $r$ with its centre at the origin where a magnetic dipole moment $m$ is placed as shown in figure. When the ring rotates at constant angular velocity about $y-$axis, electromotive force induces between its ends is

• A. $Zero$
• B. $V=\frac{{\mu }_{0}m\omega }{2\pi r}$
• C. $V=\frac{{\mu }_{0}m\omega }{4\pi r}$
• D. $V=\frac{{\mu }_{0}m\omega }{8\pi r}$

Answer 1

The correct option is B $V=\frac{{\mu }_{0}m\omega }{2\pi r}$

Radius of ring $=r$

Magnetic dipole moment $=m$

Since the ring is rotating angular momentum$=\omega$

Thus potential of the ends

$\Rightarrow$ E.M.F force$V=\frac{{\mu }_0\left(mass\right)\left(angular\right)}{length}$

For ring length$=2\pi r$

$V=\frac{{\mu }_{0}m\omega }{2\pi r}$