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)