1. LEVEL 3 ENGINEERING PRINCIPLES - MAGNETISM EQUATIONS
Magnetism Equations
Subject Equation Variables and Units
Magnetic Flux Density B =
Φ
A
B = magnetic flux density in Weber per
square meter or Tesla (Wb/m2 or T)
Φ = magnetic flux in Weber (Wb)
A = area flux passes through (m2)
mmf = magneto motive force in ampere-
turns (At)
I = current in Amps (A)
N = number of turns (t)
H = magnetic field strength (At/m)
l = length of coil / electro-magnet (m)
R = reluctance in ampere-turns per
Weber (At/Wb)
*μ0 = absolute permeability of free space
k = relative permeability
Magneto Motive Force
(analogous to voltage)
mmf = IN
Magnetic Field Strength H =
mmf
𝑙
=
IN
𝑙
Reluctance
(analogous to resistance)
R =
IN
Φ
R =
𝑙
Aμ0 𝑘
Relative Permeability 𝑘 =
B
Hμ0
Magnetic Flux Density B = 𝑘μ0H
Useful Constant Values:
*μ0 = 1.256637 x 10-6
2. Electromagnetic Induction Equations
Subject Equation Variables and Units
Force on a Current
Carrying Conductor
F = BI𝑙
F = force on current carrying conductor (N)
B = magnetic flux density in Weber per square
meter or Tesla (Wb/m2 or T)
I = current in Amps (A)
l = length of current carrying conductor (m)
T = armature toque in Newton meters (Nm)
r = armature radius in meters (m)
d = armature diameter in meters (m)
P = power in Watts (W)
Ea = EMF at armature in Volts (V)
Ia = Armature current in Amps (A)
n = rotational speed in revs per second (RPS)
EMF = induced EMF in Volts (V)
v = velocity in meters per second (m/s)
Vp = voltage (primary coil) in Volts (V)
Vs = voltage (secondary coil) in Volts (V)
Np = number of turns on primary coil
Ns = number of turns on secondary coil
L = inductance in Henries (H)
N = number of turns on inductor coil
Φ = magnetic flux in Weber (Wb)
k = relative permeability
*μ0 = absolute permeability of free space
A = cross sectional area of coil (m2)
lc = coil length in meters (m)
E = energy in Joules (J)
τ = time constant in seconds (s)
R = resistance in Ohms (Ω)
i = instantaneous current in Amps (A)
Iss = steady state current in Amps (A)
(
𝑑𝐼
𝑑𝑡
) = rate of change of current (A/s)
Armature Torque T = 2Fr = Fd
Electrical Power
(Armature)
P = EaIa
Mechanical Power
(Armature)
P = 2πnT
EMF Induced in
Current Carrying
Conductor
EMF = B𝑙v
Transformer Voltage
Ratio
Vs
Vp
=
Ns
Np
Inductance
(Self-Inductance)
L =
NΦ
I
L =
𝑘μ0N2
A
𝑙c
Energy Stored in an
Inductor E =
LI2
2
Inductor Time
Constant
(Series Resistor)
τ =
𝐿
𝑅
Inductor Energising
Current
𝑖 = Iss (1 − e
−t
τ )
Back EMF for an
Inductor
EMF = −L (
dI
dt
)
