Induction of a coil and force exerted on magnet in a magnetic field

[Detektyw]

Hi! This is my first post on this forum, and I have two questions.

First of all I'd like to mentoin that my math knowledge is at high school level + some basic calculus. Ah, and I haven't learned about (partial) differential equations yet.

My physics skills go only as far as electromagnetism and so if someone answered this question I would be really grateful for any explanations of the phenomena or algebra above the level described.

My problems are:

a) How to calculate magnetic induction (scalar) of a copper coil with an electricity source attached without a core (if someone knows how to calculate it with a core I'd like to know that too, but it's not necessary for what I'm doing now) ?

b) How to calculate the force exerted on a permanent magnet in such a coil if we assume that the coil is symmetrical and there is a current flowing through it. The preferred form would be as a function of distance from the center of the coil.

Thanks in advance.

 

[Detektyw]

Update:

I've found the solution for the simpler version of the first problem.

H = N * I/L where N is number of windings (dimensionless), I the current (amps), L the length of the coil's wire (meters).

H times permability of the magnet is the induction.

If I've mistaken somewhere, please correct me.