Inductor in simple circuit w/ graph Problem Help

[SWFanatic]

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.

 

[kamerling]

I can't see any pictures

 

[Moetasim]

As a scientist, it is important to carefully read and analyze the given information before attempting to solve the problem. Let's break down the given information and equations to better understand the problem.

The circuit in Figure 30-63 consists of a battery, resistor, switch, and inductor. When the switch is closed at t=0, the inductor will start to build up a magnetic field, causing the current to increase. The battery has an emf of 16V, which is the potential difference that drives the current through the circuit.

Figure 30-64 shows the relationship between the magnetic flux through each turn of the inductor and the current through the inductor. The slope of the graph, which is a constant 2E-4H, represents the inductance of the inductor (L). This means that for every 1 ampere (A) of current flowing through the inductor, there is a change in magnetic flux of 2E-4H (Henry).

Now, let's look at the equations provided. The first equation, L= flux/current, is the definition of inductance. It tells us that the inductance of the inductor is equal to the magnetic flux through each turn divided by the current. The second equation, emf = L|di/dt|, is known as Faraday's law and tells us that the induced emf (voltage) in the inductor is equal to the inductance multiplied by the rate of change of current. Finally, the third equation, emf = |d(flux)/dt|, is another way of stating Faraday's law, where the induced emf is equal to the rate of change of magnetic flux.

Now, to solve the problem, we need to find the rate of change of current (di/dt) at t=1.9L. This means that we need to find the slope of the current vs. time graph at t=1.9L. To do this, we can use the slope formula, which is rise/run. In this case, the rise is the change in current (di) and the run is the change in time (dt). Therefore, the slope (di/dt) at t=1.9L is equal to the change in current divided by the change in time.

To find the change in current, we can use the slope of the graph, which is 2E-