Magnetic Terms used in Magnetic Circuits – Definition & Formulas

Electrical Technology

Magnetic and Magnetism Important Terms, Definition and Formulas

Table of Contents

Magnetic Field or Magnetic Induction (B)

Magnet or Electromagnet produces a Magnetic field. The field where the magnet attracts or repels magnetic materials such as iron, steel, etc. it may be defined as a force on a moving charge,

F = q x v x B

Where

F = Force,
V = Speed of Particles,
B = magnitude of the field.

Good to Know:

It is a vector quantity and The SI Unit of magnetic Field is Tesla where, 1 Tesla = (Newton x second) / (coulomb x meter) 10,000 Gauss. The Formula for the magnetic field in SI is B = µ_○ (H+M) and in CGS is B = H+4π M.

A wire carrying a DC current or permanent magnet produces magnetostatic (Stationery) field and its magnitude and direction remain same. While Alternating current or Pulsating DC current carrying conductor creates alternating magnetic field which continuously change their direction and magnitude.

Magnetic Field Strength (H)

The amount of magnetizing force (how much force it has to magnetize, magnetic materials such as iron, steel, etc) is called Magnetic field strength which is denoted by (H). It is inversely proportional to the length of wire and directly proportional to the current passing through it. The SI unit of Magnetic Field Strength is Ampere/meter (A/m) and it is a vector quantity and the SI formula for Magnetic Field strength is

H = NI / 1c

Where 1c = magnetic path in meter.

Magnetic Flux (Φ)

In simple words, Magnetic field x area perpendicular to the magnetic field (B) is called Magnetic Flux which is denoted by Φ or Φ_m or Φ_B. Or it is the amount of magnetic field or magnetic lines of force passing through a surface like conducting area, space, air, etc. The SI Unit of magnetic flux is Wb (Weber). The Formula for finding magnetic flux in the SI system is;

Φ = BAc

Where

Ac = area in m²

And CGS unit and formula for Magnetic Flux is Maxwell (M) and Φ = BAc Ac = area in cm² respectively.

Magnetization (M)

The state of a material being magnetized or the process in which magnetic materials are magnetized. It is the density of permanent magnet or electromagnet dipole moments in magnetic materials. Or the magnetic moment (m) per unit volume (v) by a magnetic field is called Magnetization. The SI Unit of Magnetization is Ampere/meter (A/m) and it is also a vector quantity. The SI formula for Magnetization is

M = m/V

Where,

m = Total magnetic moment
And V= volume in m³.

The CGS unit and formula of Magnetization is Emu/cm³ and M = m/V respectively, where, m = Total magnetic moment, V = volume in cm³ and EMU = Electromagnetic units. It may also be defined in term of M = (N/V) x m → M = nm ……. (N/V) = n. Where, “m” is the magnetic moment and “n” is the number density of magnetic moments.

Magnetic Permeability of vacuum (µ_○)

In funny words, Perm = Permission and ability is the feature or skill to do something. I.e. permeability (µ) it is the ability of a material that how does it easily magnetize?

Magnetic Permeability of vacuum

It is the amount of resistance encountered to the magnetic field when forming in a vacuum.

The SI unit of Permeability is (H·m⁻¹), or Newton per ampere squared (N·A⁻²). The SI unit and formulas of Magnetic Permeability of vacuum is Newton/Ampere² and µ_○= 4πx10^-7 ≈ 1.2566370614 H·m⁻¹respectively. The CGS unit of magnetic permeability of vacuum is 1.

Good to know: The opposition of magnetic permeability is Magnetic Reluctivity.

Good to Know: Famous magnetic relation is B = µH where µ is permeability which is a scalar quantity, B is the magnetic field and H is magnetizing force or Magnetic Field Strength.

Inductance (L)

Inductance is the property of conductor, coil or wire which opposes the change of current flowing through it. The change of current flowing through a conductor produces a voltage called Back EMF or Electro motive force.

Even The change of current flowing through a conductor or coil produces voltage through it which is called Self induced EMF and in any nearby coils or conductors which is called Mutual inductance. The SI unit of Inductance (L) is Henry “H” and formula is

L = µ_○µ N²Ac/1c

Where

N = Turns
Ac = Area in m²
1c = magnetic path in meter

CGS unit and formula of Inductance is Henry “H” (Joseph Henry) and L = 0.4π µN²Ac/1c x10^-8 respectively

where;

L = Inductance
N = Turns
Ac = Area in cm²
1c = magnetic path in cm.

Good to Know: 1 H = 1 Wb/A (One Henry = 1 Weber per Ampere)

Self Inductance formula

L = µ_○ (N²xA)/l

Where:

L = in Henries
μ_ο = the Permeability of Free Space (4.π.10^-7)
N = the Number of turns
A = the Inner Core Area (π.r²) in m²
l = the length of the Coil in meters

Mutual Inductance formula

M = μ_ο μ_rN₁N₂A/l

Where:

µ_o = the permeability of free space (4.π.10^-7)
µ_r = the relative permeability of the soft iron core
N = in the number of coil turns
A = in the cross-sectional area in m²
l = the coils length in meters

Voltage or E.M.F (V)

The Electric Potential Difference between two points is called Voltage. Or the work done per unit charge in a static electric field to move the charge between two points, so the equation becomes as

V = W/q or E/q.

Where;

V = Voltage
E = Energy in joules
q = Charge in Coulombs

Or the electric potential energy per unit charge is called Voltage.

In Ohm’s Law, Voltage = V = I x R, Where I = Current in amperes and R = Resistance in Ohms (Ω)

The SI unit of Voltage is the Volt (V) or Joules per Coulomb. Where 1V = 1Joule/1Coulomb

The SI formula of Voltage is

V = -N dΦ/dt

Where;

N = number of coil Turns
dΦ = rate of the Change in flux
t = time

Good to know: Other related words used for Voltages and EMF are, Electrical Potential Difference, Electric Tension , Electric Pressure, potential difference, P.d, E.M.F, Electromotive force and it is a scalar quantity and it is a type of Electrical Energy.

The following table shows all the above basic terms used in magnetic circuits with SI and CGS units and formula.

Quantity	Symbol	SI Unit	SI Equation	CGS Unit	CGS Equation	Conversion Factor
Magnetic Field	B	Tesla (T)	B = µ_○(H+M)	Gauss (G)	B = H+4π M	1T = 10⁴G
Magnetic Field Strength	H	Ampere/meter (A/m)	H = NI/1c 1c = magnetic path in m	Oersted Oe	H=0.4πNI/1c 1c = magnetic path in cm	1A/m =4πx10^-3 Oe
Magnetic Flux	Φ	Weber (Wb)	Φ = BAc Ac=area in m²	Maxwell M	Φ=BAc Ac = area in cm²	1Wb =10⁸M
Magnetization	M	Ampere/meter (A/m)	M=m/V m = Total magnetic moment, V = volume in m³	Emu/cm³ Where EMU = Electromagnetic units	M=m/V m=Total magnetic moment, V = volume in cm³	1A/m = 10-³emu/cm³
Magnetic Permeability of vacuum	µ_○	Newton/Ampere²	µ_○= 4πx10^-7 ≈ 1.2566370614 H·m⁻¹	1	–	4πx10^-7
Inductance	L	Henry	L = µ_○µN²Ac/1c N = Turns Ac = Area in m² 1c = magnetic path in m	Henry	L=0.4π µN²Ac/1c x10^-8 N=Turns Ac=Area in cm² 1c = magnetic path in cm	1
Voltage or EMF	V	Volt	V = – NdΦ/dt N=Turns	Volt	V = -10^-8xNxdΦ/dt N=Turns	1