Calcady™
Home / Scientific / Electromagnetism Lorentz Force Generator

Electromagnetism Lorentz Force Generator

Isolate the explicit scalar Newton force applied to charged kinetic particles traversing combined Electrodynamic and Magnetic cross-fields.

Isolate the explicit scalar Newton force applied to charged kinetic particles traversing combined Electrodynamic and Magnetic cross-fields.

Coulombs

Accepts Scientific Notation (e.g., 1.6e-19)

V/m
Teslas
m/s
Degrees

Total Vector Substrates

Total Electromagnetic Force (F)

1.6000e-13
Newtons (N)
Electric Component0
Magnetic Component1.600e-13
Email LinkText/SMSWhatsApp

What is The Right-Hand Rule of the Universe?

The Lorentz force is the fundamental invisible hand pushing charged particles around the cosmos. It combines two radically different engines: Electric forces (which push straight forward like gravity) and Magnetic forces (which act like a bizarre cross-wind, pushing sideways completely perpendicular to the particle's movement). This mathematical cross-product is why the Earth's magnetic core deflects deadly solar radiation sideways into the atmosphere to create the Aurora Borealis.

Mathematical Foundation

The Lorentz Force Equation
F=qE+q(v×B)\mathbf{F} = q\mathbf{E} + q(\mathbf{v} \times \mathbf{B})
F\mathbf{F}= Total Lorentz Force (Newtons). The absolute sum of geometric electric and magnetic pushing forces.
qq= Fundamental electric charge of the particle (Coulombs). An electron is strictly -1.6×10^-19.
E\mathbf{E}= Electric Field vector strength (Volts/meter).
v\mathbf{v}= The physical velocity of the particle (m/s). If the particle is sitting still, magnetic forces literally cannot see it.
B\mathbf{B}= Magnetic Field vector strength (Teslas).

Laws & Principles

  • The Sine Wall: The Magnetic force relies on a mathematical sine wave angle: sin(θ). If an electron flies absolutely parallel (0°) to a magnetic field, sin(0)=0. The magnetic force drops instantly to dead zero. The electron passes through unharmed. The force is only maximized at exactly 90° completely sideways.
  • The Speed of Light Cap: Classical Lorentz math casually assumes standard Newtonian limits. If you accelerate a particle faster than 3.0 × 10^8 m/s, you violate Einstein's Theory of Relativity. The formula will spit out a number, but you are creating physically impossible fictional mass calculations in reality.

Step-by-Step Example Walkthrough

" A single positive proton (q = 1.6 × 10^-19 Coulombs) is fired at 2,000,000 m/s exactly perpendicular (90°) into a 0.5 Tesla MRI magnetic field. There is zero Electric field (E=0). "

  1. 1. Calculate Electric base: (1.6e-19) * 0 = 0 Newtons.
  2. 2. Analyze trig boundary: sin(90°) = exactly 1.
  3. 3. Multiply Magnetic variables: 2,000,000 * 0.5 * 1 = 1,000,000.
  4. 4. Multiply by Particle Charge: (1.6e-19) * 1,000,000 = 1.6e-13 N.
Final Result: The MRI field strikes the microscopic proton with exactly 1.6e-13 Newtons of sideways force, mathematically dominating its trajectory and forcing it into a circular orbit.

Quick Answer: How does the Lorentz Force Calculator work?

It executes complex vector multiplication to find total force on a moving charge. You enter the particle's charge, speed, the electric/magnetic field strengths, and the entry angle. The engine instantly isolates the scalar Newton force applied to the particle, highlighting exactly how much force comes from the E-field vs the B-field.

Mathematical Formulas

F = q * [E + (v * B * sin(θ))]

This scalar equation computes the magnitude of the force. q is charge, E is electric field, v is velocity, B is magnetic field, and θ is the angle between velocity and the magnetic field vectors.

Common Particle Charges Matrix (Reference)

Fundamental particles and their physical injection variables.

Particle Charge Magnitude (C) Behavior in E-Field Behavior in B-Field
Proton+ 1.602 × 10⁻¹⁹Accelerates with fieldDeflects per Right-Hand Rule
Electron- 1.602 × 10⁻¹⁹Accelerates against fieldDeflects opposite to Proton
Alpha (He⁺⁺)+ 3.204 × 10⁻¹⁹Accelerates with fieldDeflects per Right-Hand Rule
Neutron0UnaffectedUnaffected

Engineering Use Cases

Particle Accelerators (CERN)

The Large Hadron Collider relies entirely on the Lorentz force curve. Massive electric fields are used to push protons near the speed of light along the track, while gigantic cryogenic magnets provide the perpendicular B-field force required to keep the protons turning in a perfect 27-kilometer circle without smashing into the walls.

Mass Spectrometry

Chemists strip an electron off an unknown molecule, give it velocity, and fire it into a magnetic field. Because the Lorentz force pushes moving charges sideways, lighter molecules get thrown into a tight curve while heavy ones make a wide curve. By measuring where they hit the wall, chemists calculate the exact molecular weight.

Physics Best Practices

Do This

  • ✓Remember neutral immunity. If a particle has no charge (like a neutron or a standard atom of Carbon), the q value is strictly 0. Multiplying through the entire force equation guarantees the final Newton force is exactly zero. EMF fields do not affect neutral geometry.

Avoid This

  • ✗Don't ignore the speed of light limit. Classical Lorentz calculators like this one use Newtonian framing. If you input a velocity greater than 299,792,458 m/s, the calculator will warn you that you are violating Einstein's relativity. Mathematical results for FTL speeds are functionally meaningless.

Frequently Asked Questions

What is the Right-Hand Rule?

It is a physical trick to find the 3D direction of the magnetic force. If you point your right thumb in the direction of velocity (v) and your fingers in the direction of the magnetic field (B), the force pushes straight out of your palm. (For negative electrons, you use your left hand).

Why does a stationary charge feel no magnetic force?

Magnetism is mathematically a relativistic effect. A magnetic field is literally generated by moving charges. If an electron is sitting still relative to the field (velocity equals 0), the v component in the equation zeroes out the entire magnetic term. The electron will only feel the electric field.

How do I enter scientific notation?

Our inputs accept standard 'e' notation used in computer science. To input an electron's charge (-1.602 × 10⁻¹⁹), simply type '-1.602e-19' into the charge field. The engine will instantly process the microscopic value correctly.

Why are the outputs in Scientific Notation?

Fundamental particles have mass approaching zero, meaning it takes virtually zero force (Newtons) to rapidly accelerate an electron. Typing out 0.00000000000016 Newtons is unreadable. We output '1.6e-13 N' for maximum academic clarity.

Related Scientific Calculators