Are My Flux Calculations for Toroids and Solenoids Correct?

[radicaled]

This is more a theoretical question than a practical one.
Basically I want to know if the formulas I arrive for the flux of a Toroid and a Solenoid are correct

Leaving aside the integration part this is the basic formula for the flux
[itex]\phi = BNA[/itex]
B = magnetic field
N = number of turns of the solenoid/toroid
A = Area

So for the solenoid I arrive to this:
[itex]B = \mu nI[/itex] -> n = N/L
[itex]A = 2\pi r(r+l)[/itex] this is the area for a cylinder
[itex]\phi = \mu nINA = \frac{\mu IN^{2}}{L}2\pi r(r+L)[/itex]

For the toroid I arrive to this:
[itex]B = \frac{\mu NI}{2\pi r}[/itex]
[itex]\phi = \int BNdr = \frac{\mu IN^{2}}{2\pi}ln\frac{b}{a} [/itex]

 

[lippyka]

Where a and b are the inner and outer radii of the toroid.So my question is, Are these formulas correct? Yes, the formulas are correct.