A wire forming one complete sine curve is moved in the xy-plane with velocity V⃗=Vₓî+Vᵧĵ in a uniform magnetic field B⃗=-B₀k̂. Find the motional emf between ends P and Q.

Question

G1 Physics · Accepted Answer

For uniform translation, ε=∫(V⃗×B⃗)·dℓ⃗. Here B⃗=-B₀k̂. Over one complete sine curve, only the net endpoint separation contributes; the result is ε=ℓVᵧB₀. Hence option B.