## Magnetism

Units are denoted in green

### Magnetic field

Teslas(T) (N/A*m)

N

### 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

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

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)

V N→ # of turns in coil

### Inductance

Henry(H) (T*m²/A)

### Inductance of a solenoid

l→ length, n→ # turns per unit length

V

rise of current
time constant
decay of current

J

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

/dd>

A

### 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

### Charge oscillations

C Q→ amplitude of variations, φrarr; phase constant

A

J

J

### RLC circuit equation

SOLUTION: ω' = √(ω² - (R/2L)²) C