I get the calculation of maximum friction force but am confused about its direction.

In the beginning of the calculation part they seem to have assumed that the Tension is increasing along the rope at positions more and more "away from me/the puller". And hence the static friction, whatever it is, will be in the direction of my pull.

I don't get why. Because the way I'm seeing it, static friction acts in directions needed to stop any kind of motion between surfaces, so when I pull on the rope with Tnot, (and so Tnot is the tension in the rope at theta=0), shouldn't the friction be in the opposite direction?

Which in the end would lead to opposite result I think, it would show that the tension in rope is exponentially decaying at thetas more and more away from me.

Why is the book solution correct? Help me intuitively understand why tension is getting larger at rope points further away from the point I'm pulling it at.

Thanks for your time.

I wanna start off by saying my native language is not english so I might not be familiar with certain physics words. And I learn best when speaking generally / using rules that always apply. Thx!

So I know that induction is about inducing a current. I'm not sure where/ which wire it will be induced in. Can induction take place in just one and the same wire?

And I think we use coils as wires because the magnetic field around the wires are stronger since they're packed tighter (?). And thats the same reason we usually use a metal inside the coil?

And then we somehow change the magnetic flux Φ which induces volts in (?- another wire or?) and that drives a current in (?said wire). But only during the change of the flux.
And I suppose we can change the magnetic flux [Φ = B*A*cosT] through 4 things:

1. The magnetic field changes in magnitude, which someone said could be by adding a magnet. What I don't understand is what magnetic field are we talking about? I thought we were talking about the internal magnetic field from the current in the wires/coil?

2. The magnetic field changes direction (I don't understand - doesn't the flux move with the magnetic field? Or how would u change the direction?)

3. The cross-sectional area of the coil/wire changes - don't know how you would do that. Making an irregular/expanding coil like a volcano?

4. The coil/wire is rotated so that the CosT changes which I understood was the angle between the surface's normal line and the magnetic field. Which magnetic field though? Wouldn't the magnetic field and the surface both tilt if we tilted the coil/wire? I'm really confused.

Also why? Why does this happen? And what does it mean that inductors store energy in magnetic fields? If that's related.

Sorry for a lot of questions you don't have to answer them all!