In this case you should apply the law of electromagnetic induction of Faraday.
Ԑi = N(Δφ/Δt)
Ԑi, is the EMF induced in the coil.
N, is the number of turns of the coil where the EMF is induced.
Δφ = BS, is the variation that occurs in the magnetic flux. In this case, we will consider that the cross section S is equal in both coils.
Δt, is the time during which the flux is changing.
Let's call #1 to the largest coil and #2 the smaller coil. Then we see that the variation of the magnetic flux in the coil #1, induces an EMF in the coil #2.
So, we can write the Faraday law, for coil #2, in the following way:
Ԑi = N2(Δφ2/Δt) = N2[Δ(B1S2)/Δt)]
The magnetic field of the coil #1 is:
B1 = μ0nI, where μ0 is the magnetic permeability of vacuum, n is the number of turns per unit length of the coil and I is the current.
Substituting in the equation of the EMF and considering that only varies the current, we have:
Ԑi = N2[Δ(μ0nIS2)/Δt)] = (N2μ0nS2)(ΔI/Δt)
Ԑi = (50)(4π*10^-7)(2*10^3)(0.31)(3.99/5.9)
Ԑi = 1.11*10^-2 V
The current is calculated by applying OHM's law:
I = Ԑi/R = (1.11*10^-2)/(4.09*10^-3)
I = 2.7 A