Magnetism

Units are denoted in green

Magnetic field

Teslas(T) (N/A*m)

Magnetic force

N

Circulating charged particle

Force on a current

N L→ length of current-carrying wire

Magnetic dipole moment

A*m² N → # of turns, A→ area enclosed by coil

Torque on a current coil

N*m All 3 are vectors

Magnetic potential energy

J

Biot-Savart law

T
μ0→ Permeability constant (μ0 = 4π x 10-7 T*m/A)

Magnetic field due to current in an infinitely-long, straight wire

T R→ distance from wire

Magnetic field due to current in a semi-infinite straight wire

T

Magnetic field due to current in a circular arc of wire

T At center of arc, φ→ arc's central angle in radians

Force between two parallel currents

N Force on wire b due to field from a, d→ wire separation

Ampere's law

Closed loop integral, B and ds are vectors

Ideal solenoid

T n→ number of turns per unit length

Toroid

T N→ number of turns

Coil as a magnetic dipole

T z→ distance from center of loop, B and μ are vectors

Magnetic flux through an area

Webers(Wb) (T*m²)

Faraday's law

V N→ # of turns in coil

Inductance

Henry(H) (T*m²/A)

Inductance of a solenoid

l→ length, n→ # turns per unit length

Self-induced EMF

V

RL circuit

rise of current
time constant
decay of current

Magnetic energy

J

Magnetic energy density

Gauss' law for magnetic fields

Wb

Spin magnetic dipole moment

S→ spin angular momentum vector

Bohr magneton

J/T h→ Planck's constant (h = 6.63 x 10-34 J*s)

Orbital magnetic dipole moment

Lorb→ orbital angular momentum vector

Maxwell's law of induction

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Displacement current

A

Ampere-Maxwell law

Induced magnetic field inside a circular capacitor

T R→ radius of capacitor plates, r→ distance from center

Induced magnetic field outside a circular capacitor

T r→ distance from center

Angular frequency of LC oscillations

LC oscillation equation

Charge oscillations

C Q→ amplitude of variations, φrarr; phase constant

Current oscillations

A

Stored energy in the electric field of a capacitor

J

Stored energy in the magnetic field of a capacitor

J

RLC circuit equation

SOLUTION: ω' = √(ω² - (R/2L)²) C