Is Current I1 Constant in Mutual Inductance Systems?

[BlackMelon]

Hello,

Homework Statement

All variables and known data are given in one of the attached files.
Does the figure 8.2 show that the current I1 is constant?

My assumption is based on Lenz's law. What I mean is that if the I1 varies, there will be changes in magnetic fluxes(delta-B) produced by I1. The circuit C2 will oppose this change by forming its current I2; consequently, there will be fluxes, which are generated by I2, that will penetrate C1 also. Therefore, the assumption will not happen if I1 is constant.

Homework Equations

depicted in one of the attached files.

The Attempt at a Solution

I both study the mutual inductance in the textbook containing the following pictures and Lenz's law. Also, I try to combine them together. I just want to check my understanding.

 

[Merlin3189]

I'm not sure what, if anything, you are asking here, but here are my comments.

Does the figure 8.2 show that the current I1 is constant?

No. I₁ can vary.

My assumption ... if the I1 varies, there will be changes in magnetic fluxes(delta-B) (Φ₁?) produced by I1. The circuit C2 will oppose (but not nullify) this change by forming its current I2; consequently, there will be fluxes, which are generated by I2 , that will penetrate C1 also. Therefore (? I see no logical connection here.), the assumption will not happen if I1 is constant. (AFAI can see, that must be true: if I₁ is constant, then it cannot change. But that is trivial.)

But there is nothing to stop I₁ from changing. If I₁ changes, then there will be an induced emf in C₂ and I₂ will change. The flux change caused by this will oppose the change in I₁, but not prevent it. Here, there is only partial linkage between the coils, so there is plenty of stray or leakage flux which can be changed by I₁. But even where there is tight coupling between the coils, unless the flux linkage is 100% and the coil C2 is a perfect conductor, the change in I₂ will not be enough to completely prevent the change in I₁.

Lenz's law tells you only the sense in which induced emfs and currents act, not their magnitude.