Magnetic flux:

The magnetic flux is defined as the number of magnetic field lines passing through a closed surface

Flux can be expressed as

$\varphi =BA\cos \theta$

ϕ  is the magnetic flux

B is the magnetic flux density

A is the area

θ is the angle between the surface area vector of a surface and magnetic field

Given that, θ = 90°

$\Rightarrow \varphi =BA\cos 90=0$

Coulomb’s law:

The force between two point charges is along the line joining between them is directly proportional to the product of point charges and inversely proportional to the square of the distance between them:

$F\propto \frac{Q_1{Q}_2}{R^2}$

Q1 & Q2 must be static or at rest.

The distance (R) between two-point charges R is very large compared to the dimension of a charged body

$\therefore F=\frac{K{Q}_1{Q}_2}{R^2}$

Where $K=\frac{1}{4\pi {\epsilon }_o}=9\times {10}^{9}m/F$

$F=\frac{1}{4\pi {\epsilon }_o}\frac{Q_1{Q}_2}{R^2}$

${\epsilon }_o=\frac{1}{4\pi f}\frac{Q_1{Q}_2}{R^2}\frac{C^2}{N-m^2}$

${\epsilon }_o=8.854\times {10}^{-12}\cdot \frac{F}{m}=\frac{{10}^{-9}}{36\pi }\frac{F}{m}$

Coulomb force follows the superposition principle

Application:

When the separation (R) between two charges is made four times, then force between them is

$F\propto \frac{{}_1}{R^2}$

∴ Force is decreases sixteen times

Magnetomotive force (MMF):

The current flowing in an electric circuit is due to the existence of electromotive force similarly magnetomotive force (MMF) is required to drive the magnetic flux in the magnetic circuit. The magnetic pressure, which sets up the magnetic flux in a magnetic circuit is called Magnetomotive Force.

The strength of MMF is equal to the product of the current and no. of turns of the coil

MMF can be expressed as

MMF = N I = (Flux) x (Reluctance)

The SI unit of MMF is ampere-turn (AT)

Magnetomotive force (MMF):

The current flowing in an electric circuit is due to the existence of electromotive force similarly magnetomotive force (MMF) is required to drive the magnetic flux in the magnetic circuit. The magnetic pressure, which sets up the magnetic flux in a magnetic circuit is called Magnetomotive Force.

The strength of MMF is equal to the product of the current and no. of turns of the coil

MMF can be expressed as

MMF = N I = (Flux) x (Reluctance)

The SI unit of MMF is ampere-turn (AT).

Calculation:

The Airgap length l_g = 2.5 mm

Effective area A = 200 cm²

air gap $s_g=\frac{l_g}{{\mu }_{o}A}=\frac{2.5\times {10}^{-3}}{4\pi \times {10}^{-7}\times 200\times {10}^{-4}}$ = 9.95 × 104

MMF = Flux × reluctance = 0.015 × 9.95 × 10⁴ = 1492.5 AT

MMF:

The strength of MMF is equal to the product of the current and no. of turns of the coil

MMF can be expressed as

MMF = N I = (Flux) x (Reluctance)

The SI unit of MMF is ampere-turn (AT)

Calculation:

Given that, MMF = 30 Amp-turns

Magnetic flux = 40 Wb

Reluctance = MMF / flux = 30 / 40 Amp-turns / Wb

Permeance is the reciprocal of reluctance.

B-H relation:

The relation between magnetic field intensity (H) and magnetic flux density (B) is

B = μ H Wb/m²

μ = The magnetic permeability

μ_o = Absolute permeability

μ_r = Relative permeability of the medium

Magnetic field intensity: It is magnetic field strength represented in terms of a number of magnetic field lines (flux) passing through a unit area perpendicular to the field lines.

$H=\frac{MMF}{l}=\frac{NI}{l}$

The energy loss associated with hysteresis is proportional to the area of the hysteresis loop. As the area of the hysteresis loop for a specimen is found to be large, the hysteresis loss in this specimen is also large.

Hysteresis loss occurring in a material is,

$W_h=\eta \times B_m^{1.6}\times f\times V$

Where η is hysteresis constant

f is frequency or number of cycles per second

B_m is magnetic flux density

V is the volume of the core

Curie temperature:

• For the ferromagnetic materials, below the Curie temperature, the atoms are aligned and parallel causing spontaneous magnetism
• Above the Curie temperature, the material is paramagnetic as the atoms lose their ordered magnetic moments when the material undergoes a phase transition

The magnetic flux density is given by

B = μ₀ (H + M)

Where, M = magnetization of the medium and H = magnetic field strength

μ_r is the relative permeability of a medium

⇒ μ₀μ_rH = μ₀ (H + M)

⇒ μ_rH = H + M

⇒ (μ_r - 1) H = M

$\Rightarrow \left({\mu }_r-1\right)=\frac{M}{H}$

$\Rightarrow {\mu }_r=1+\frac{M}{H}$