Lorentz Force
Calculate the magnetic force on a moving charged particle using the Lorentz force equation F = qvB sin(α). Free electromagnetism calculator with charts and formula breakdown.
About This Calculator
The Lorentz Force Calculator computes the magnetic force exerted on a moving charged particle using the fundamental equation F = qvB sin(α). This calculator is essential for physics students, researchers, and engineers working with electromagnetism, particle physics, and magnetic field interactions.
The Lorentz force law states that a magnetic field exerts a force on any moving charged particle. The magnitude of this force depends on four factors: the particle's electric charge (q), its velocity (v), the strength of the magnetic field (B), and the angle between the velocity and magnetic field vectors (α). The force is maximized when the particle moves perpendicular to the magnetic field (α = 90°) and drops to zero when moving parallel to the field lines (α = 0°).
This tool uses the standard SI unit system: charge in coulombs (C), magnetic field in teslas (T), velocity in meters per second (m/s), angle in degrees (°), and outputs force in newtons (N). The calculator handles the trigonometric conversion automatically and provides a detailed breakdown of each component.
How It Works
The calculation follows these steps: (1) the angle α is converted from degrees to radians, (2) sin(α) is computed, and (3) the Lorentz force is calculated as the product of charge, velocity, magnetic field, and sin(α). For example, an electron (q = 1.602 × 10⁻¹⁹ C) moving at 1 × 10⁶ m/s through a 0.5 T magnetic field at 90° experiences a force of 8.01 × 10⁻¹⁴ N.
Applications of Lorentz Force
The Lorentz force has numerous real-world applications: in particle accelerators like cyclotrons and synchrotrons to steer high-energy particles; in mass spectrometers to separate ions by their mass-to-charge ratio; in electric motors and generators where current-carrying wires experience force in magnetic fields; in cathode ray tubes and old CRT displays; and in plasma physics for magnetic confinement fusion research. Understanding the Lorentz force is fundamental to electromagnetism and modern physics.
Frequently Asked Questions
What is the Lorentz force?
The Lorentz force is the force exerted by a magnetic field on a moving charged particle. It is calculated using the formula F = qvB sin(α), where q is the charge in coulombs, v is the velocity in m/s, B is the magnetic field strength in teslas, and α is the angle between the velocity and magnetic field vectors.
How do I calculate the Lorentz force?
Enter the particle charge in coulombs, the magnetic field strength in teslas, the velocity in meters per second, and the angle between the velocity and magnetic field in degrees. Click Calculate to get the force in newtons using F = qvB sin(α).
What is the Lorentz force equation?
The Lorentz force equation is F = qvB sin(α), where F is the force in newtons, q is the charge in coulombs, v is the velocity in m/s, B is the magnetic field in teslas, and α is the angle between the velocity and magnetic field. The force is maximal when α = 90° and zero when α = 0°.
What is the direction of the Lorentz force?
The Lorentz force acts perpendicular to both the velocity vector and the magnetic field vector. For a positively charged particle, use the right-hand rule: align your thumb with velocity, index finger with the magnetic field, and your middle finger points in the direction of the force. For negative charges, reverse the direction.
What are practical applications of the Lorentz force?
The Lorentz force is used in cyclotrons and particle accelerators to steer charged particles, in mass spectrometers to identify atoms and molecules, in electric motors and loudspeakers to convert electrical energy into motion, and in railgun technology for electromagnetic propulsion.
Is the Lorentz force calculator free?
Yes, this Lorentz force calculator is completely free to use with no registration required. You can share your calculation results via URL.
What units does the Lorentz force calculator use?
This calculator uses SI units: charge in coulombs (C), magnetic field in teslas (T), velocity in meters per second (m/s), angle in degrees (°), and force in newtons (N).
What happens if the angle between velocity and magnetic field is 0?
When the angle α is 0° (the particle moves parallel to the magnetic field lines), sin(0°) = 0, so the Lorentz force is zero. The particle continues moving along the magnetic field lines without deflection.