Moving Charges and Magnetism — Formula Sheet

F = qvB sin θ

r = mv/qB

ω = 2πν = qB/m

p = v∥T = 2πmv∥/qB

dB = (μ0/4π) (I dl × r)/r^3

|dB| = (μ0/4π) (I dl sin θ)/r^2

μ0/4π = 10^-7 T m/A

μ0ε0 = 1/c^2

B = μ0 I R^2/[2(x^2+R^2)^(3/2)]

B0 = μ0I/2R

B = (μ0/4π)(2m/x^3)

B = (μ0/4π)(m/x^3)

The force on a charge q moving with velocity v in electric and magnetic fields is F = q[E(r) + v × B(r)].

For a straight conductor in an external magnetic field, the force is F = I l × B.

If velocity is perpendicular to the magnetic field, a charge moves in a circle with radius r = mv/qB.