LEVEL 3 ENGINEERING PRINCIPLES - MAGNETISM EQUATIONS Magnetism Equations Subject
Equation
Magnetic Flux Density
B=
ÎŚ A
Variables and Units B = magnetic flux density in Weber per square meter or Tesla (Wb/m2 or T) ÎŚ = magnetic flux in Weber (Wb)
Magneto Motive Force (analogous to voltage)
Magnetic Field Strength
mmf = IN
H=
mmf IN = đ?‘™ đ?‘™
A = area flux passes through (m2) mmf = magneto motive force in ampereturns (At) I = current in Amps (A) N = number of turns (t)
R= Reluctance (analogous to resistance)
IN ÎŚ
l = length of coil / electro-magnet (m)
R=
đ?‘™
R = reluctance in ampere-turns per
AÎź0 đ?‘˜
Weber (At/Wb)
Relative Permeability
B đ?‘˜= HÎź0
Magnetic Flux Density
B = đ?‘˜Îź0 H
Useful Constant Values:
*Îź0 = 1.256637 x 10-6
H = magnetic field strength (At/m)
*Îź0 = absolute permeability of free space k = relative permeability
Electromagnetic Induction Equations Subject
Equation
Variables and Units
Force on a Current Carrying Conductor
F = BIđ?‘™
Armature Torque
T = 2Fr = Fd
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) Electrical Power (Armature)
P = Ea Ia
Mechanical Power (Armature)
P = 2Ď€nT
EMF Induced in Current Carrying Conductor
EMF = Bđ?‘™v
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)
Transformer Voltage Ratio
Vs Ns = Vp Np
EMF = induced EMF in Volts (V) v = velocity in meters per second (m/s) Vp = voltage (primary coil) in Volts (V)
L= Inductance (Self-Inductance)
NÎŚ I
Vs = voltage (secondary coil) in Volts (V) Np = number of turns on primary coil Ns = number of turns on secondary coil
2
L=
đ?‘˜Îź0 N A đ?‘™c
L = inductance in Henries (H) N = number of turns on inductor coil ÎŚ = magnetic flux in Weber (Wb)
Energy Stored in an Inductor Inductor Time Constant (Series Resistor) Inductor Energising Current
2
E=
LI 2
Ď„=
k = relative permeability *Îź0 = absolute permeability of free space A = cross sectional area of coil (m2)
đ??ż đ?‘…
lc = coil length in meters (m) E = energy in Joules (J) −t
Ď„ = time constant in seconds (s)
đ?‘– = Iss (1 − e Ď„ )
R = resistance in Ohms (Ί) i = instantaneous current in Amps (A)
Back EMF for an Inductor
dI EMF = −L ( ) dt
Iss = steady state current in Amps (A) đ?‘‘đ??ź
(đ?‘‘đ?‘Ą) = rate of change of current (A/s)