Electromagnetic Induction

(1) Induced EMF:

$ e = – N dϕ/dt $ volts

e = B x l x v volts

(2) Inductance:

$ L = {N ϕ}/{I} $ Henry

$$ e = -L [{dI}/{dt}] $$

(3) Coefficient of self-inductance:

$ L = {N^2 μ_0 μ_r a}/{l} $

N = Number of turns
l = length of magnetic circuit
a = Cross sectional area of magnetic circuit

(4) Mutual Inductance:

$ e_2 = -M {dI_1}/{dt} $

$M = {N_2 K ϕ_2}/{I_1}$

$ M = {N_1 N_2 μ_0 μ_r1 a_1 }/{l_1} $

(5) Coefficient of Coupling (K):

$M = K √{L_1 L_2}$

$K = M/M_{max}$

$M_{max}= √{L_1 L_2}$

(6) Energy stored in magnetic field:

$$ E = 1/2 LI^2 $$

(7) Energy stored per unit volume:

$ E = 1/2 B^2/μ = 1/2 μ_0 H^2 $ Joules/$m^3$

(8) Eddy current loss:

$ P_e = k_e B_max_^2 f^2 t^2 v $ watts