A vertical ring of radius r and resistance R falls vertically with speed v, remaining in contact with two vertical, frictionless, resistance-free rails joined at the top. A uniform magnetic field B is perpendicular to the ring and rails. The current in the upper rail section PQ is nBrv/R. Find n. [See Image.]
Physics · Mixed Chapter
JEE Mains

Question

A vertical ring of radius r and resistance R falls vertically with speed v, remaining in contact with two vertical, frictionless, resistance-free rails joined at the top. A uniform magnetic field B is perpendicular to the ring and rails. The current in the upper rail section PQ is nBrv/R. Find n. [See Image.]

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Step 1 — A straight segment connecting the two contact points spans the ring diameter 2r. Step 2 — As the ring moves with speed v perpendicular to the field, the motional emf between its left and right contact points is ℰ = B(2r)v = 2Brv. Step 3 — The ring has uniform resistance R, so each semicircular branch has resistance R/2. Both semicircles develop the same contact-to-contact emf ℰ and feed current through the resistance-free rail closure. Step 4 — Current delivered by one semicircle is I₁…