Question

A thin semicircular conducting ring of radius R is falling with its plane vertical in a horizontal magnetic induction $\overrightarrow{B}$ (fig.). At the position MNQ the speed of the ring is v and the potential difference development across the ring is

• A. Zero
• B. $\frac{Bv\pi R^{2}}{2}$andM is at higher potential
• C. πRBv and Q is at higher potential
• D. 2RBv and Q is at higher potential

Answer 1

Answer: (D)

2RBv and Q is at higher potential

Answer 2

Suppose in time t vertical distance travelled by ring is v × t so change in area $\frac{dA}{dt} = 2Rvt$

∴ $e = - \frac{d\varphi}{dt} = - B\frac{dA}{dt}$

⇒ |e| = 2RBv

and by Flemings right hand rule. Q is at higher potential.