Calculating the Inductance of a Toroidal Solenoid

[Cockroach]

This one is giving me a headache. I thought I had the right solution after a long time of scrolling back and forth in the physics book... I think the biggest problem for me is how do I use that 1.26x10-6 N/A^2 for the permeability of free space. If you can answer this you might want to post the whole procedure of solving this problem, cause my problem might be that everything I'm trying is wrong!

A toroidal solenoid has a cross-sectional area of 0.420 cm^2 , a mean radius of 12.6 cm, and 1850 turns. The space inside the windings is filled with a ferromagnetic material that has a relative permeability of 500.
Calculate the inductance of the solenoid. (You can ignore the variation of the magnetic field across the cross section of the toroid.) Use 1.26×10-6 N/A^2 for the permeability of free space.

Please help me. I'm not trying to get someone to do my homework for me, I just didn't see any other alternatives after all this time of trying! Thank you.

 

[gnome]

$$\mu_0$$ = permeability of free space is just a constant you use to find B, the magnetic field inside the toroid. If the interior of the toroid was a vacuum you would just use $$\mu_0$$ but for your toroid you will use $$500\mu_0$$ because of the given relative permeability of the metal core.

So, for your toroid,
$$B = \frac{500\mu_0NI}{2\pi{r}}$$
N is the number of turns, I is the current and r is the mean radius.

Next, you have to figure out $$\phi_B$$, the magnetic flux through each turn, and then you can solve for the inductance L.

 

[outandbeyond2004]

Do you not understand what "relative" means?

 

[ragnarr]

How do I find I, the current to find B?

 

[Doc Al]

inductance is independent of current

How do I find I, the current to find B?

You won't need the current to calculate the inductance. When you use the expression that gnome provided for B to calculate the inductance, the current will drop out. (You'll need to know the definition of inductance.)