Magnetic force and torque
т = m × B
F = ∇ (m · B)
т: magnetic torque applied on an object (Nm)
m: magnetic moment vector (Am2)
B: magnetic flux density (T)
F: magnetic force applied on an object (N)
Lorentz force (or electromagnetic force)
F = q ( E + v × B )
F: force (N)
q: electric charge (C)
E: external electric field (V/m)
v: velocity (m/s)
B: magnetic field (T)
Newton’s second law of motion
F = ma
F: net external force applied on an object (N)
m: object mass (kg)
a: acceleration of the object (m/s2)
Mass-energy equivalence
E = mc2
E: equivalence energy of an object (J)
m: object mass (kg)
c: speed of light (m/s)
Ampère’s circuital law
∇ × B = μ0 J
∇ ×: the curl operator
B: magnetic flux density (T)
μ0: vacuum permeability (H/m)
J: the total current density (A·m−2)
Reynolds number (Re)
Re = ρuL / μ = uL / ν
ρ: fluid density (kg·m−3)
u: fluid speed (m·s−1)
L: characteristic linear dimension (m)
μ: dynamic viscosity (Pa·s or N·s·m−2 or kg·(m·s)−1)
ν: kinematic viscosity (m2·s−1)
Young-Laplace equation
Δp = – γ · ( 1 / R1 + 1 / R2 )
Δp: Laplace pressure, the pressure difference across the fluid interface (Pa)
γ: surface tension (F · m−1)
R1 and R2: principle radii of curvature (m)