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Walk-through

How to Use This Calculator

3 steps

1

Pick the field you're working with

Use the Magnetic Force tab if you only care about a charge moving through a magnetic field, the Electric Force tab for a charge sitting in an electric field, or the Combined tab for both fields acting on the charge at once.

2

Enter charge, velocity, field, and angle

Fill in the charge q (in coulombs), and — for magnetic force — the velocity v (m/s), magnetic field B (tesla), and the angle θ between the velocity and field vectors, in degrees. For electric force, just charge and the electric field E (V/m). The calculator updates instantly as you type.

3

Read the force and interpretation

The result card shows the force in newtons, plus a plain-language interpretation — for example, whether you're at the maximum magnetic force (θ = 90°) or getting no magnetic force at all (θ = 0° or 180°). On the Combined tab, the magnetic and electric contributions are broken out separately since they act in different directions.

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Reference

Formula & Methodology

3 formulas

Lorentz force

F = qE + qvB·sinθ

The total force F (in newtons) on a charge q (coulombs) is the sum of the electric force qE and the magnetic force qvB·sinθ. E is the electric field (V/m), v is the charge's speed (m/s), B is the magnetic field strength (tesla), and θ is the angle between the velocity and the magnetic field, in degrees.

Magnetic force alone

F_magnetic = qvB·sinθ

The magnetic component of the Lorentz force. It's maximum when velocity and field are perpendicular (θ = 90°, sinθ = 1) and zero when they're parallel or antiparallel (θ = 0° or 180°, sinθ = 0). The direction of this force is always perpendicular to both v and B, given by the right-hand rule.

Electric force alone

F_electric = qE

The electric component of the Lorentz force. Unlike the magnetic force, it doesn't depend on the charge's velocity — a stationary charge in an electric field still feels this force, acting along the field direction (or opposite it, for a negative charge).

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Glossary

Key Terms Explained

7 terms

Lorentz force The total electromagnetic force on a charged particle, combining the electric force (qE) and the magnetic force (qvB·sinθ). Named after Dutch physicist Hendrik Lorentz.

Moving charge A charged particle (electron, proton, ion, or any charged object) traveling with some velocity through a region containing an electric field, a magnetic field, or both.

Magnetic field (B) A vector field, measured in tesla (T), that exerts a force on moving charges. Unlike an electric field, a magnetic field only pushes on charges that are already in motion, and the push is always perpendicular to both the field and the velocity.

Electric field (E) A vector field, measured in volts per meter (V/m), that exerts a force on any charge — moving or stationary. The force is qE, directed along the field for a positive charge and opposite the field for a negative charge.

Velocity (v) The speed and direction of the charged particle's motion, measured in meters per second (m/s). Only the magnetic force depends on velocity — the electric force does not.

Right-hand rule A way to find the direction of the magnetic force: point your fingers in the direction of velocity, curl them toward the magnetic field, and your thumb points in the direction of the force on a positive charge (reverse it for a negative charge).

Angle (θ) The angle between the velocity vector and the magnetic field vector, in degrees. It controls the sinθ term in the magnetic force formula — 90° gives the maximum force, 0° or 180° gives zero force.

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Scenarios

Real-World Examples

3 worked examples

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Physics student

Electron moving through a magnetic field

Charge (q) 1.6 × 10⁻¹⁹ C Velocity (v) 1,000,000 m/s Magnetic field (B) 0.5 T Angle (θ) 90°

With velocity perpendicular to the field, the magnetic force is F = qvB·sinθ = (1.6×10⁻¹⁹)(1,000,000)(0.5)(1) = 8.0×10⁻¹⁴ N — small in absolute terms, but enormous relative to the particle's mass, which is exactly why magnetic fields can bend electron beams into tight circles.

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Lab instructor

90° gives the maximum magnetic force

Charge (q) 1.6 × 10⁻¹⁹ C Velocity (v) 1,000,000 m/s Magnetic field (B) 0.5 T Angle (θ) 0° vs. 90°

At θ = 0° (velocity parallel to the field), sinθ = 0 and the magnetic force vanishes entirely, no matter how fast the charge moves. At θ = 90°, sinθ = 1 and the force reaches its maximum — this is why particle accelerators arrange the field perpendicular to the beam.

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Engineer

Combining electric and magnetic fields

Charge (q) 1.6 × 10⁻¹⁹ C Velocity (v) 1,000,000 m/s Magnetic field (B) 0.5 T, θ = 90° Electric field (E) 1,000 V/m

On the Combined tab: electric force qE = 1.6×10⁻¹⁶ N and magnetic force qvB·sinθ = 8.0×10⁻¹⁴ N, giving a total of about 8.16×10⁻¹⁴ N. Because the electric force runs along E while the magnetic force is perpendicular to both v and B, this total is a magnitude sum — a velocity selector (used in mass spectrometers) is designed so these two forces exactly cancel in opposite directions instead.

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Deep Dive

Understanding the Lorentz Force Calculator

3 chapters · 4 min read

The Lorentz force describes how electric and magnetic fields push on a moving charged particle — it's the foundation behind everything from CRT televisions and mass spectrometers to particle accelerators and the aurora borealis. This calculator computes the electric contribution, the magnetic contribution, and the combined total from the charge, velocity, field strengths, and angle.

How the Lorentz Force Calculator works

The Lorentz force law states F = qE + qvB·sinθ. The electric term, qE, acts on any charge regardless of motion — it points along the field for a positive charge and opposite the field for a negative one. The magnetic term, qvB·sinθ, only acts on a moving charge, and its direction is always perpendicular to both the velocity and the magnetic field (found with the right-hand rule), which is why magnetic forces curve a particle's path into a circle or helix rather than speeding it up or slowing it down in a straight line.

Inputs and what they mean

Charge (q) is the particle's electric charge in coulombs — an electron carries about −1.6×10⁻¹⁹ C, a proton about +1.6×10⁻¹⁹ C. Velocity (v) is the particle's speed in meters per second, relevant only to the magnetic force. Magnetic field (B) is the field strength in tesla, and angle (θ) is measured between the velocity and field vectors — 90° gives the strongest magnetic push, while 0° or 180° (velocity parallel or antiparallel to the field) gives none at all. Electric field (E), in volts per meter, drives the electric force independently of speed or angle.

Limits and edge cases

This calculator reports the magnitude of each force component and sums them for the Combined tab — it does not track direction as a full 3D vector, since the electric force acts along E while the magnetic force acts perpendicular to both v and B, and their combined direction depends on the specific geometry of the setup. For relativistic speeds (a meaningful fraction of the speed of light), the underlying physics needs a relativistic momentum correction that this calculator does not apply. For the force on a charge from another charge at rest (rather than from a field), see the Coulomb's Law calculator; for the changing-flux voltage that induces currents, see Faraday's Law.

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Questions

Frequently Asked Questions

6 questions

What is the formula for the Lorentz force?+

F = qE + qvB·sinθ, where q is the charge in coulombs, E is the electric field in volts per meter, v is velocity in meters per second, B is the magnetic field in tesla, and θ is the angle between velocity and the magnetic field.

When is the magnetic force at its maximum?+

The magnetic force qvB·sinθ is maximum when the velocity is perpendicular to the magnetic field, meaning θ = 90° and sinθ = 1.

What direction does the magnetic force point?+

Always perpendicular to both the velocity and the magnetic field, found with the right-hand rule: point your fingers along v, curl them toward B, and your thumb points along the force on a positive charge (the opposite direction for a negative charge).

What happens when both fields act on a charge at the same time?+

The electric and magnetic forces add together, but not necessarily along the same line — the electric force runs along E, while the magnetic force is perpendicular to both v and B. The Combined tab reports both components and their magnitude sum.

What units does the calculator use?+

Charge in coulombs (C), velocity in meters per second (m/s), magnetic field in tesla (T), electric field in volts per meter (V/m), angle in degrees (°), and the resulting force in newtons (N).

When is the magnetic force zero even if the charge is moving?+

When the velocity is parallel or antiparallel to the magnetic field — θ = 0° or 180° — sinθ = 0 and there's no magnetic force, regardless of how fast the charge is moving or how strong the field is.

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Lorentz Force Calculator

Academic & Standard References:

How to Use This Calculator

Pick the field you're working with

Enter charge, velocity, field, and angle

Read the force and interpretation

Formula & Methodology

Key Terms Explained

Real-World Examples

Physics student

Lab instructor

Engineer

Understanding the Lorentz Force Calculator

How the Lorentz Force Calculator works

Inputs and what they mean

Limits and edge cases

Frequently Asked Questions

Get a branded PDF of your results

Lorentz Force Calculator

Academic & Standard References:

How to Use This Calculator

Pick the field you're working with

Enter charge, velocity, field, and angle

Read the force and interpretation

Formula & Methodology

Key Terms Explained

Real-World Examples

Understanding the Lorentz Force Calculator

How the Lorentz Force Calculator works

Inputs and what they mean

Limits and edge cases

Frequently Asked Questions

Get a branded PDF of your results

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