## Magnetism

What is a permanent magnet? This is a ferromagnetic material like iron, nickel or cobalt that has the ability to attract other pieces of the same material.

A permanent magnet will orient itself in the Earth's North-South direction when freely suspended and thus we say a magnet's north pole is the end that will point towards the North and the magnet's south pole is the end that will point towards the South.

The magnetic field is the area around the magnet. This is the area around which the strength of the magnet (magnetic force) is detected. The magnetic field cannot be seen or felt. Through various experiments, it has been shown that the magnetic field exists as lines of flux that flow from the north pole to the south pole and they form complete loops. These lines of flux are very close when the magnet is strong and vice versa.

If you put two magnets close to each other, unlike poles will attract, and like poles will repel.

### Magnetic flux and flux density

Magnetic flux, $$\phi$$ is the amount of lines of force produced by a magnetic source. It is measured in weber, Wb.

Magnetic flux density, $$B$$ is the amount flux passing a given area which is perpendicular to the flux direction. It is measured in the tesla, T.

$\textrm{Magnetic flux density} = \dfrac{\textrm{magnetic flux}}{\textrm{area}}$

$B = \dfrac{\phi}{A} \textrm{tesla}.$

$1T = 1Wb/m^2$

### Magnetomotive force (m.m.f.) and magnetic field strength (H)

Magnetomotive force (m.m.f.) is the cause of the existence of a magnetic flux in a magnetic circuit.

$$m.m.f. = NI$$ where $$N$$ is the number of conductors or turns and $$I$$ is the current. It is expressed in ampere-turns.

Magnetic field strength (magnetic force), $$H = \dfrac{NI}{l}$$ ampere per metre. Where $$l$$ is the length of the flux path in metres.

$$m.m.f. = NI = Hl$$ amperes.

### Permeability

This is the ratio of the magnetic flux density, $$B$$ to the magnetising force, $$H$$.

Permeability $$µ = \dfrac{B}{H} = µ_0µ_r$$

$$µ_0 = 4π \times 10^{-7}$$H/m is the permeability of air non-magnetic materials. This is considered free space and its $$µ_r = 1$$.

$µ_r = \dfrac{\textrm{flux density in material}}{\textrm{flux density in vacuum}}$

### Reluctance, S

This is the magnetic resistance of hte magnetic circuit in the presence of magnetic flux.

$$S = \dfrac{m.m.f or F_m}{\phi} = \dfrac{NI}{\phi} = \dfrac{HL}{BA} = \dfrac{l}{\dfrac{B}{A}A} = \dfrac{l}{µ_0µ_rA}$$ measured in $$A/Wb$$

Ferromagnetic materials have very low relucatnce and thus can be used as magnetic shields to protect components or materials within the shield from magnetic fields.

#### Series relucatances

Just like resistances in series: $$S = S_1 + S_2 + … + S_n$$