Inductor in simple circuit w/ graph Problem Help

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The problem involves a circuit with an inductor, a battery of 16 V, and a graph showing magnetic flux through each turn versus current. The key equations relate inductance to flux and current, as well as the electromotive force (emf) to the rate of change of current. The user expresses confusion about interpreting the graph, particularly in determining the flux per turn and understanding the slope's implications. They question if the slope represents the relationship between the rate of change of flux and current. Clarification on these points is needed to solve for the rate of change of current at the specified time.
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Homework Statement


In Figure 30-63, the inductor has 26 turns and the ideal battery has an emf of 16 V. Figure 30-64 gives the magnetic flux through each turn versus the current i through the inductor. If switch S is closed at time t = 0, at what rate di/dt will the current be changing at t = 1.9L?
Figure 30-63 is a simple circuit with a battery, resistor, switch, and inductor.
Figure 30-64 is a flux vs. current graph, with a constant slope of 2E-4H.


Homework Equations


L= flux/ current
emf = L|di/dt|
emf = |d(flux)/dt|


The Attempt at a Solution


I am rather lost. The graph shows flux per turn over current, but how do I know what the flux of each turn is? The graph is just an increasing slope with seemingly no boundries. Also, isn't the slope just (d(flux)/dt)/(di/dt)? And if so, wouldn't (di/dt) just be 1, or have I forgotten how to read graphs? Thanks for any help.
 
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