Question
A vertical ring of radius rand resistance $$R$$ falls vertically. It is in contact with two vertical rails which are joined at the top. The rails are without friction and resistance. There is a horizontal uniform magnetic field of magnitude $$B$$ perpendicular to the plane of the ring and the rails. When the speed of the ring is $$v,$$ the current in the top horizontal of the rail section is
A.
0
B.
$$\frac{{2Brv}}{R}$$
C.
$$\frac{{4Brv}}{R}$$
D.
$$\frac{{8Brv}}{R}$$
Answer :
$$\frac{{8Brv}}{R}$$
Solution :
$$I = \frac{{2Brv}}{{\frac{R}{2}}} = \frac{{4Brv}}{R}$$
Current in the top horizontal $$ = 2I = \frac{{8Brv}}{R}.$$
$$I = \frac{{2Brv}}{{\frac{R}{2}}} = \frac{{4Brv}}{R}$$
Current in the top horizontal $$ = 2I = \frac{{8Brv}}{R}.$$
