π What is Magnetic Force?
The magnetic force is the force exerted on a moving charged particle due to a magnetic field. This force is perpendicular to both the velocity of the charged particle and the magnetic field. The magnitude of the magnetic force is given by:
$F = qvB \sin(\theta)$
Where:
- βοΈ $F$ is the magnitude of the magnetic force.
- β $q$ is the charge of the particle.
π v is the velocity of the particle.
- 𧲠$B$ is the magnetic field strength.
- π $\theta$ is the angle between the velocity vector and the magnetic field vector.
π What is Lorentz Force?
The Lorentz force is the total electromagnetic force exerted on a charged particle. It is the sum of the electric force and the magnetic force.
$F = qE + qvB \sin(\theta)$
Where:
- β‘ $F$ is the total Lorentz force.
- β $q$ is the charge of the particle.
- π‘ $E$ is the electric field strength.
- π v is the velocity of the particle.
- 𧲠$B$ is the magnetic field strength.
- π $\theta$ is the angle between the velocity vector and the magnetic field vector.
π Magnetic Force vs. Lorentz Force: A Detailed Comparison
| Feature |
Magnetic Force |
Lorentz Force |
| Definition |
Force on a moving charge due to a magnetic field. |
Total electromagnetic force: Sum of electric and magnetic forces. |
| Source |
Magnetic field only. |
Electric field and magnetic field. |
| Formula |
$F = qvB \sin(\theta)$ |
$F = qE + qvB \sin(\theta)$ |
| Effect on Charge |
Changes the direction of motion (circular or helical path). Does no work. |
Changes both the speed and direction of motion. Can do work. |
| Conditions |
Requires a moving charge in a magnetic field. |
Requires a charged particle in electric and/or magnetic fields. |
β¨ Key Takeaways
- π The magnetic force is only a component of the Lorentz force.
- β‘ When only a magnetic field is present, the magnetic force *is* the Lorentz force.
- π‘ The Lorentz force accounts for both electric and magnetic influences on a charged particle.