Lorentz Force Calculator

Calculator Inputs

Charge q

Charge Unit

Velocity Unit

Velocity Vx

Velocity Vy

Velocity Vz

Electric Field Unit

Magnetic Field Unit

Use negative charge values for electrons or negatively charged particles.

Electric Field Ex

Electric Field Ey

Electric Field Ez

Magnetic Field Bx

Magnetic Field By

Magnetic Field Bz

Formula Used

Vector Lorentz force:
F = q(E + v × B)

Electric contribution:
F_electric = qE

Magnetic contribution:
F_magnetic = q(v × B)

Magnetic magnitude form:
|F_magnetic| = |q|vBsinθ

The calculator treats velocity, electric field, and magnetic field as 3D vectors. It first computes the cross product v × B, then multiplies by charge q for magnetic force, adds qE for electric force, and finally reports the net vector and magnitude.

Positive and negative charges are handled directly. A negative charge reverses the force direction relative to the same field and motion vectors.

How to Use This Calculator

Enter the particle charge and choose its unit.
Enter the velocity components Vx, Vy, and Vz in one consistent unit.
Enter electric field components Ex, Ey, and Ez.
Enter magnetic field components Bx, By, and Bz.
Click the calculate button to get electric, magnetic, and total force results.
Review the vector table, magnitude, direction unit vector, and angle between velocity and magnetic field.
Use the CSV or PDF buttons to export your result summary.
Check the Plotly graph to compare x, y, and z force components visually.

Example Data Table

Charge	Velocity Vector (m/s)	Electric Field (V/m)	Magnetic Field (T)	Approx. Net Force
2 µC	[3,000,000, 0, 0]	[1200, 500, 0]	[0, 0.15, 0]	≈ 0.900004 N
-1.6 nC	[0, 2500, 600]	[0, 800, 0]	[0.02, 0, 0.01]	Direction reverses with negative charge
5 mC	[12, 18, 6]	[150, 90, 30]	[0.004, 0.001, 0.002]	Useful for vector force practice

FAQs

1. What does the Lorentz force describe?

It describes the total force on a charged particle due to electric and magnetic fields. The electric field pushes along field direction, while the magnetic field acts perpendicular to both velocity and magnetic field.

2. Why do I need vector components?

Lorentz force is naturally a vector quantity. Using x, y, and z components lets you model motion and fields in any direction, not only simplified textbook cases.

3. What happens when the charge is negative?

The force direction reverses. Magnitude depends on absolute charge size, but the sign changes the vector direction of both electric and magnetic force terms.

4. When is the magnetic force zero?

It becomes zero when velocity is zero, magnetic field is zero, charge is zero, or velocity is parallel or antiparallel to the magnetic field, making sinθ equal to zero.

5. Why does the calculator show angle between velocity and magnetic field?

That angle controls magnetic force magnitude through |q|vBsinθ. A larger perpendicular component produces larger magnetic force, while a parallel direction produces none.

6. Can I use N/C instead of V/m for electric field?

Yes. N/C and V/m are equivalent electric field units in this context, so the calculator treats them with the same conversion factor.

7. What does the Plotly graph show?

It compares x, y, and z components for electric, magnetic, and total force. This helps you see which axis dominates the final Lorentz force result.

8. Is this useful for physics homework and lab analysis?

Yes. It supports consistent units, vector decomposition, export tools, and visual checks, making it practical for coursework, reports, and quick validation of hand calculations.