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Magnetic Field

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Magnetic Field

Basic Concepts:

A current carrying wire produces a magnetic field in the area around it.

A time changing magnetic field induces a voltage in a coil (wire) if is passes through the coil (transformer)

A moving wire in the presence of a magnetic field has a voltage induced in it (generator)

A current-carrying wire in the presence of a magnetic field has a force induced on it (motor).

The Basic Law:

Ampere’s Law

H : Magnetic field intensity (A-turns/m)

Ampere’s Law in a very simple form

Ampere’s Law in a coil

N : turns

i : Current (A)

lc: mean length (m)

H : Magnetic field intensity (A-turns/m)

Important: H is the effort that a current is putting to produce a magnetic field.

The magnetic field will depend on the material of the core.

Now we define:

B : Magnetic flux density (T=Wb/m2) , (Tesla= Webers per square meter)

Where :

: Magnetic permeability (H/m) , (henrys per meter)

and :

: Magnetic flux

The permeability of free space is:

Now we define relative permeability of different materials:

The higher the relative permeability, the more flux. For steel it is 2000-6000. Materials with high values of relative permeability

In summary we can write:

Defining new variables and constants:

: magnetomotive force (A-turns), then we have:

: reluctance (A-turns/Wb)

: permeance (Wbs/ A-turn)

Then we have:

In summary in a magnetic field we have:

Compare this formula with Ohm’s law in electric circuits:

Example 1:

Given : i=1 A, N=100, lc=40 cm, A= 100 cm2 r =5000

Calculate : F, H, B, , and

Assume 5% increase in effective

Cross-sectional area

for fringing effect

Calculate total reluctance and current

Assume 4% increase in effective

Cross-sectional area

for fringing effect

Calculate the flux density in each of the legs

The similarities lead us to Magnetic Circuits theory. This means we can use the rules we had for series and parallel resistances.

Fringing effect means that when we have an air gap, the effective cross sectional area of the air gap is larger than the cross-sectional area of the iron-core

What do we do with the fringing effect?

1- Add the air gap length to each dimension

2- Assume the effective area is 5% more than the cross-sectional are of the iron-core