Sure, we can solve this problem by using Faraday's law of electromagnetic induction.
Step 1: Convert the EMF into volts. As we're given 17 mV (millivolts), we convert it to volts by multiplying by 10^-3. So, 17 mV = 17 * 10^-3 = 0.017 V.
Step 2: Write down the other given quantities. There are 314 turns on the coil and the current is changing at a rate of 14.5 A/s.
Step 3: Apply Faraday's law of electromagnetic induction. The emf (electromotive force) in a circuit is equal to the negative rate of change of magnetic flux through the circuit (emf = -d(phi)/dt). The minus sign is a result of Lenz's law, which states that currents are induced in such a way as to oppose the change causing them.
Step 4: Substitute the values into the formula. To find the magnetic flux, ϕ (in Weber, Wb), through each turn of the coil, we rearrange Faraday's law to give:
ϕ = -emf / turns / rate of change of current
We substitute our given values into the equation to find:
ϕ = -0.017 / 314 / 14.5
Step 5: Solve for ϕ to give the magnetic flux per turn. Using a calculator, we find ϕ is approximately equal to -3.73 x 10^-6 Wb. This is the magnetic flux through each turn of the coil at the instant when the current is 2.09 A.
Please note, having a negative result for the magnetic flux is completely normal in this situation because of Lenz’s law. What's important is the magnitude of this flux, not its sign. The negative sign simply indicates that the flux is decreasing.