I've learned in school that the force in a coil is $F=kx$, linear on how much the coil is stretched. Two questions:
Is it always linear for every shape of a coil? Does it remain linear if we increase the radius of the coil, increase the length between loops and so on?
Can we deduce the value of $k$ based on the geometry of the coil?
The motivation is that I know how to deduce the inductance of a coil based on its shape, but I haven't seen that calculation done to deduce the $k$ in Hooke's Law.