Δt= [tex] \frac{NB_0 \pi a^2 }{IR} [/tex]
This because ε = dΦ/dt, and emf is a voltage so it can also be written as dΦ/dt = IR
Because ΔΦ= ABcosθ for each of the N loops and cosθ is just 1 here only A needs to be replaced, and it can be replaced with A=πr^2, which makes that part of the equation ΔΦ_m=N*B0*πa^2
