Question

In figure, there is a conducting ring having resistance $R$ placed in the plane of paper in a uniform magnetic field $B_0$. If the ring is rotating in the plane of paper about an axis passing through point $O$ and perpendicular to the plane of paper with constant angular speed $\omega$ in clockwise direction, then

• A. point $O$ will be at higher potential than $A$
• B. the potential of point $B$ and $C$ will different
• C. the current in the ring will be zero
• D. the current in the ring will be $2B_0\omega r^2/R$
• E. answer required

Answer 1

Answer: (C)

the current in the ring will be zero

The ring can be seen as two rod OCA and OBA in parallel.

The motional emf will be induced between O and A = $\frac{1}{2}B(2r{)}^2\omega =2B{r}^2\omega$ with A positibe wrt O

In both the paths from O - C - A ; and from O - B - A , potential increases as one moves from point O to point A.
Point B and C are at same potential due to symmetry.
As there is no return path, no current flows even though a potential is developed between points O and A