# Understanding the math of inductance

1. ### Jayen

2
Hello all,

I do apologize if this is in the wrong section as this is my first post. If I have posted in the wrong area please let me know.

I have a basic understanding of the concept of inductance but have read many formulas which I think are trying to express the same idea but from various sources. I would like to put my understanding forward and have it corrected where need be.

Faraday law determines the amount of emf (Voltage) which will be induced by a coil of wire into an electromagnetic field.

emf (voltage induced) = -N Δ$\Phi$ / Δt

where N = number of turns in the coil
$\Phi$ = Flux density (BA) measured in Teslas
B = I think this depends on the type of coil, for a solenoid B = Mo n I
where Mo = 4pi x 10-7
n = number of turns in coil / length of the coil
I = current
A = Cross sectional area of the coil (pi r2)
t = time

There are a few variables I would think may be a factor in this equation which are not included. Firstly the permeability of the core and secondly the frequency at which the magnetic field changes.

Any help in understand these equations would be greatly appreciated.

Thankyou.

2. ### Simon Bridge

15,259
This is a good overview.
http://hyperphysics.phy-astr.gsu.edu/hbase/electric/farlaw.html

There is only one relation - the different formulas are usually due to the different geometries when the rule is applied.

The variation of the B field is accounted for in the flux term ... permiability of the region the field is in counts in the reverse situation - finding a B field about a current.
http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/magcur.html

3. ### mabs239

86
ΔΦ / Δt term also take frequency into account. More the frequency, more will be the value of ΔΦ / Δt. Flux is due to magnetic motive force which is a function of current. Suppose current is i=cos(2*pi*f*t), taking rate of change of this current will move 2*pi*f outside and voltage will have a direct relation with frequency.

4. ### Okefenokee

245
$\Phi$ is flux not flux density. Once you integrate B (flux density) over and area you get flux ($\Phi$). It may not seem like much of a distinction but it's important. Flux density is a vector field with magnitude and direction (like the flow of water currents). Flux is a scalar value (like the total amount of water flow through the mouth of a bay).

For a solenoid, B = $\mu NI/l$

In general, B = $\mu H$ (Sometimes you have to account for the magnetization of the material so this one is not always true)

So the magnetic field strength is, H = $NI/l$

And flux density is, B = $\mu_0 \mu_r H$

Where $\mu_r$ is the relative permeability of the material and $\mu = \mu_0 \mu_r$

5. ### Jayen

2
Thanks very much for your replies. I think this has clear things up for me but just to make sure I am 100% clear in my head I want to see if I am correct (this is not homework).

If I have a solenoid of 10 cm total length, 100 turns, iron core (200 μ) and radius of 4cm with 1500W @ 1500V 120Hz AC. Would the following be correct?

emf = -100 ΔΦ / Δt
B = 200 x 100 x 100 / 0.1 (200 000 T)
A = 0.00503m2
Φ = 1006 Tm2

emf = -12 120 481

I have also seen B = μN2A/l and I would assume this relates to a solenoid. Could someone please elaborate how the two differ.

6. ### Okefenokee

245
Your result is 12 million volts for a little solenoid?

Current is a function of time in AC. Your result should be a function of time too.

Have you studied Calculus? Do you know how to take a derivative?