Magnetic force on moving charge
F⃗ = q(v⃗ × B⃗)
Magnetic force magnitude
F = q v B sinθ
Magnetic force on current carrying conductor
F⃗ = I(L⃗ × B⃗)
Force magnitude on conductor
F = I L B sinθ
Radius of circular path
r = m v / (q B)
Time period of charged particle
T = 2π m / (q B)
Frequency of revolution
f = q B / (2π m)
Angular frequency
ω = q B / m
Pitch of helical path
p = v⃗_parallel T
Velocity selector condition
qE⃗ = q v⃗ B⃗
Velocity selector speed
v = E / B
Biot–Savart law (magnitude)
dB = (μ₀ / 4π) (I dl sinθ / r²)
Biot–Savart law (vector)
B⃗ = (μ₀ / 4π) (I (dl⃗ × r⃗) / r³)
Magnetic field due to long straight wire
B⃗ = μ₀ I / (2π r)
Magnetic field at centre of circular loop
B⃗ = μ₀ I / (2 R)
Magnetic field at centre of N-turn coil
B⃗ = μ₀ N I / (2 R)
Magnetic field on axis of circular coil
B⃗ = μ₀ I R² / (2 (R² + x²)³ᐟ²)
Ampere’s circuital law
∮ B⃗ · dl⃗ = μ₀ I_enclosed
Magnetic field due to a toroid
B = μ₀ N I ⁄ (2π r)
Force between two parallel current-carrying conductors
F ⁄ L = μ₀ I₁ I₂ ⁄ (2π d)
Definition of ampere
F ⁄ L = 2 × 10⁻⁷ N m⁻¹
Magnetic dipole moment (current loop)
m⃗ = I A n̂
Magnetic dipole moment (N-turn coil)
m⃗ = N I A n̂
Torque on a magnetic dipole
τ⃗ = m⃗ × B⃗
