Electric & Magnetic Flux, Density & Field Intensity Formulas

Electrical Technology

Electric Flux, Magnetic Flux, Electric Density, Magnetic Density, Electric Intensity and Magnetic Intensity Formulas & Equations

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Electric Flux Formula:

Electric flux is the electric field lines passing through an area A. It’s a vector quantity.

Φ_E = EA

Φ_E = EA cosθ

Where

Φ_E= Electric flux
E = Electric field
A = Area of the surface
θ = Angle between E and A

Non Uniform Electric Filed

dΦ_E = E dA

Electric flux for a closed Gaussian surface

Φ_E = ∯_s E dA = Q/ε₀

Where

Φ_E= Electric flux
E = Electric field
A = Area of the surface
Q = electric charge inside the surfaces of A
ε₀ = permittivity of free space (also known as universal or electric constant which is equal to ε₀ ≈ 8.854 187 817… x 10⁻¹² F·m⁻¹.)

The above equations is one of the four Maxwell’s equations also known as Gauss’ law related to an electric field.

Electric Flux Density Formula:

The electric flux per unit area is called the electric flux density.

D = Φ_E /A

Other forms of equations for electric flux density are as follow:

D = εE = q/4πr²

E = q/4πεr²

E = q/4πε_rε₀r²

D = ε_rε₀E

Where:

D = Density
Φ_E = Electric flux
A = Area

It is a scalar quantity and the unit is C/m² i.e surface charge density “σ”.

Electric Field Intensity Formula:

Force per unit charge is known as electric field intensity.

E = F/Q

Where:

E = Electric Field Intensity
F = Force
Q = Electric Charge

The electric filed strength in volt per meter formula is as follow:

ε = e/d

Magnetic Flux Formula:

The number of magnetic lines passing through area A is known as Magnetic flux.

Φ_b = BA cosθ

Where

Φ_b = magnetic flux
B = Magnetic field
A = area
θ = angle between B and A

It is a vector quantity and the general form of magnetic flux can be calculated by using the following equation:

Φ_B = ∫∫_A B dA

Magnetic Flux Density Formula:

The magnetic flux per unit area is called magnetic flux density in Tesla (webers per metre²) and it is a vector quantity.

B = Φ/A

Where:

B = Magnetic Flux Density
Φ = Magnetic Flux
A = Area

Magnetic Field Intensity Formula:

Magnetic field strength or magnetic field intensity can be calculated by using the following equations

H = I/(2πr)

H = F_m/l_e … Ampere per meter.

H = B/μ₀ – M

Where:

H is the magnetic field intensity or magnetic field strength
B is the flux density
M is the magnetization
μ₀ is the permittivity
l is the length
F is the MMF (Magnetic motive force)