Magnetic Field and Forces Equations

Physical Quantities

Quantity

Symbol

Scalar/Vector

Units

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)

/

Equations Summary

Equation

Formula

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