Magnetic Field and Forces Equations

Magnetic field

$\mathbf{B}$

Vector

Tesla (T)

Current

$I$

Scalar

Ampere (A)

Permeability of free space

$\mu_0$

Scalar

T/A

Distance from the wire

$r$

Scalar

Meter (m)

Current loop radius

$R$

Scalar

Meter (m)

Length

$\ell$

Scalar

Meter (m)

Angle

$\theta$

Scalar

Radians (rad)

Force

$\mathbf{F}$

Vector

Newton (N)

Charge

$q$

Scalar

Coulomb (C)

Number of turns in the coil

$N$

Scalar

None

Speed

$v$

Scalar

Meter per second (m/s)

Potential Difference

$V$

Scalar

Volt (V)

Mass

$m$

Scalar

Kilogram (kg)

Torque magnitude

$\tau$

Scalar

Newton-meter (N\m)

Angle between field and coil

$\phi$

Scalar

Radians (rad)

Magnetic moment

$M$

Vector

Ampere-square meter (A/m²)

Magnetic field of straight wire

$B = \frac{\mu_0 I}{2 \pi r}$

Magnetic field of a wire loop

$B = \frac{\mu_0 I}{2 R}$

Magnetic force on a current carrying wire

$F = I \ell B \sin(\theta)$

Force between two wires carrying current

F

Force on a moving charge

$F = q v B \sin(\theta)$

Path radius of a charge moving in magnetic field

r = \frac{m v}{\left

Particle mass in a mass spectrometer

m = \frac{\left