\[F=qvB\sin\theta\]
Variables
Fmagnetic Lorentz force (N)
qelectric charge (C)
vparticle velocity (m/s)
Bmagnetic field strength (T)
thetaangle between velocity and magnetic field (rad)
Description
What is this formula?
This formula calculates the magnetic force acting on a charged particle moving through a magnetic field. The force direction is perpendicular to both the velocity and the magnetic field.
When to use it
Use this equation when analyzing charged particle motion in magnetic fields, electric motors, particle accelerators, and plasma physics.
Example
An electron moves at 3×10^6 m/s perpendicular to a magnetic field of 0.25 T. Calculate the magnetic force magnitude.
Data:
q = 1.602×10^-19 C
v = 3×10^6 m/s
B = 0.25 T
theta = 90° = pi/2 rad
Formula:
F = q*v*B*sin(theta)
Substitution:
F = (1.602×10^-19)*(3×10^6)*0.25*sin(pi/2)
Result:
F = 1.20 × 10^-13 N
Applications
- Particle accelerators
- Electric motors
- Plasma confinement
- Space physics
- Electromagnetic systems