Lorentz's law force, also known simply as the Lorentz force, is the fundamental electromagnetic force exerted on a charged particle moving through an electric and magnetic field.
Understanding the Lorentz Force
The Lorentz force describes the total electromagnetic force acting on a charged particle due to its interaction with an electromagnetic field. Named after the Dutch physicist Hendrik A. Lorentz, this force is crucial for understanding how charged particles behave in electric and magnetic environments, forming the basis for many technologies from electric motors to mass spectrometers.
The Lorentz Force Equation
The entire electromagnetic force F on a charged particle is given by the Lorentz force equation:
$$
\mathbf{F} = q\mathbf{E} + q(\mathbf{v} \times \mathbf{B})
$$
Here's a breakdown of the variables in the equation:
| Symbol | Description | Unit (SI) |
|---|---|---|
| F | The total electromagnetic force | Newton (N) |
| q | The electric charge of the particle | Coulomb (C) |
| E | The external electric field vector | Volts per meter (V/m) |
| v | The instantaneous velocity vector of the particle | Meters per second (m/s) |
| B | The external magnetic field vector | Tesla (T) |
| ($\times$) | The vector cross product | N/A |
Components of the Lorentz Force
The Lorentz force is composed of two main parts:
Electric Force Component ($q\mathbf{E}$)
This part of the force is exerted on the charged particle solely by the electric field E. It acts in the same direction as the electric field if the charge q is positive, and in the opposite direction if q is negative. This component of the force is independent of the particle's velocity.
Magnetic Force Component ($q(\mathbf{v} \times \mathbf{B})$)
This component describes the force exerted on the charged particle by the magnetic field B. Key characteristics include:
- Velocity Dependence: This force only acts on a charged particle when it is moving relative to the magnetic field. If the particle is stationary (v = 0), there is no magnetic force.
- Direction: The magnetic force is always perpendicular to both the velocity vector v and the magnetic field vector B, as determined by the right-hand rule for positive charges (or left-hand rule for negative charges).
- No Work Done: Since the magnetic force is always perpendicular to the particle's velocity, it does no work on the particle, meaning it cannot change the particle's kinetic energy, only its direction of motion.
Key Characteristics and Applications
The Lorentz force is fundamental to many areas of physics and engineering:
- Particle Trajectories: It governs the path of charged particles in electromagnetic fields, crucial in devices like cathode ray tubes (CRTs), mass spectrometers, and particle accelerators.
- Electric Motors and Generators: The interaction between magnetic fields and moving charges (or current-carrying wires) under the influence of the Lorentz force is the principle behind electric motors (force on current-carrying conductors) and generators (voltage induced by changing magnetic flux).
- Hall Effect: This phenomenon, used in magnetic field sensors, is a direct consequence of the Lorentz force acting on charge carriers in a conductor.
For more in-depth information, you can refer to resources like Britannica's entry on Lorentz Force.
