Find the inductance and a current of a coil

[awesome2999]

Hi everybody, i have got a question,any help will be much appreciated

A ferrite ring core has a slot cut in it such that the plane of the slot contains the axis of the toroid. It is wound with 26 turns.

i have attached the picture of the this problem.

Relative permeability = 680
Bsat = 0.38T

Ignoring leakage and fringing:

What is the inductance of the coil?

At what current does the ferrite saturate

the equation I'm using is N^2/((lair/MoMr*Aair)+(l iron/MoMr*Airon))

l air is 0.0003m
Aair = Airon= 1.22518E-3 i calculated this one
i'm not sure for liron shoud i use 0.0039*pi and substruct from lair. but still i don't get the right answer.

the right answer should be is L=0.000139 H and I=5.5796 A

for the current still don't get the answer right. I'm using B/MoMr=H and then H=NI/2Pi*r

please.any help will be much appreciated.

 

[jbsteele]

thanks a lot. The inductance of the coil can be calculated using the equation: L = (N^2 * μo * μr * A) / l, where N is the number of turns, μo is the permeability of free space, μr is the relative permeability of the core material, A is the cross-sectional area of the core material, and l is the mean length of the winding. In this case, the mean length of the winding is equal to the circumference of the toroid, which is 2πr. The cross-sectional area of the core material is its area times the width of the slot. So, the inductance of the coil can be calculated as: L = (26^2 * 4π * 680 * (πr^2 * w)) / (2πr) where r is the radius of the toroid and w is the width of the slot. The current at which the ferrite saturates can be calculated using the equation: I= (Bsat * μo * μr * A) / (2π * l), where Bsat is the saturation flux density of the core material, μo is the permeability of free space, μr is the relative permeability of the core material, A is the cross-sectional area of the core material, and l is the mean length of the winding. In this case, the mean length of the winding is equal to the circumference of the toroid, which is 2πr. The cross-sectional area of the core material is its area times the width of the slot. So, the current at which the ferrite saturates can be calculated as: I = (0.38 * 4π * 680 * (πr^2 * w)) / (2π * 2πr) where r is the radius of the toroid and w is the width of the slot.