Can someone explain to me the properties of a soleinoid?

Question

Please list what the variables represent in these equations:

B = mv/qr

B = u(N)(I)

B = gauss strength, I = amps, what are the rest?

- I assume this equation is for a simple solenoid, what if an iron core is added like in an electric magnet? How will this change?

Answer 1

B = magnetic field strength

I = electric current

m = mass of a charged particle or object

v = velocity of the charged object or particle

q = charge of the particle or object

r = radius of orbit of the charged particle or object around the magnetic field line

u = magnetic permeability

N = number of turns of the solenoid

An iron core will increase the magnitude of the magnetic field.

EDIT: Adding an iron core will change the magnetic permeability. The permeability of free space is 4π x 10^-7 T·m/A, but that doesn't apply to a solenoid filled with air or anything else.