Calculator Inputs
Enter values in SI units. Negative components are allowed. Use scientific notation like -3.2e-6 when needed.
Formula Used
The Lorentz force on a particle with charge q moving with velocity v in electric and magnetic fields is:
F = q(E + v × B)
- F is the total force vector (newtons).
- E is the electric field vector (N/C).
- B is the magnetic field vector (tesla).
- v × B is the cross product, giving direction by the right‑hand rule.
- This calculator also reports Fₑ = qE and Fₘ = q(v × B) separately.
How to Use This Calculator
- Enter the charge q in coulombs, including the sign.
- Provide the three components of the electric field Ex, Ey, Ez.
- Enter velocity components vx, vy, vz for the moving particle.
- Enter magnetic field components Bx, By, Bz in tesla.
- Click Calculate to show results above the form.
- Use the export buttons to download a CSV or PDF report.
Example Data Table
| q (C) | E (N/C) | v (m/s) | B (T) | F (N) | |F| (N) |
|---|---|---|---|---|---|
| 1.6e-19 | [1000, 0, 0] | [2.0e5, 0, 0] | [0, 0.25, 0] | [1.6e-16, 0, 0] | 1.6e-16 |
| -1.6e-19 | [0, 800, 0] | [0, 2.0e5, 0] | [0, 0, 0.3] | [9.6e-15, -1.28e-16, 0] | 9.6009e-15 |
| 2.0e-6 | [0, 0, 50] | [120, 40, 0] | [0.01, 0, 0] | [0, 0.0008, 0.0001] | 0.0008062 |
Values are illustrative and may be rounded.
Lorentz Force Guide
1) What the Lorentz force represents
The Lorentz force describes how electric and magnetic fields push on a charged particle. In SI units, charge is in coulombs, fields are in N/C and tesla, and the resulting force is in newtons. Because the equation is vector‑based, both magnitude and direction matter for real motion.
2) Why vector components are essential
Many practical problems are three‑dimensional: a beam of ions, a plasma drift, or a conductor in a field. Entering Ex, Ey, Ez, vx, vy, vz, and Bx, By, Bz lets you model orientation directly. The cross product v × B automatically encodes the right‑hand rule direction.
3) Electric contribution qE
The electric term is proportional to the field vector itself. Since 1 N/C equals 1 V/m, a uniform field of 10,000 V/m between plates produces 10,000 N/C. A particle with charge 2.0e‑6 C would feel 0.02 N in that field, before any magnetic effects are included.
4) Magnetic contribution q(v × B)
The magnetic term depends on motion and orientation. Its magnitude is |q| v B sinθ, so it vanishes when velocity is parallel to the magnetic field. For context, Earth’s magnetic field is about 25–65 µT, while laboratory magnets can range from 0.1 T to several tesla, and MRI systems commonly operate around 1.5–3 T.
5) Typical values and unit discipline
Electrons and protons have charges ±1.602e‑19 C, while macroscopic charged particles can be microcoulombs or higher. Velocities may span from meters per second in fluids to 106–107 m/s for accelerated electron beams. Keeping consistent SI units prevents scaling errors and makes exports reusable.
6) Real‑world applications
This calculator supports scenarios such as beam steering in cathode‑ray systems, ion separation in mass spectrometers, cyclotron motion in accelerators, and drift predictions in plasma devices. In electrical engineering, Lorentz forces also appear in motor torque models and in forces on conductors carrying current in strong fields.
7) Reading the results effectively
The output separates electric and magnetic contributions so you can see which dominates. When |Fₘ| is much larger than |Fₑ|, trajectories tend to curve strongly; when |Fₑ| dominates, acceleration aligns with the electric field. The magnitude |F| is useful for quick comparisons across cases.
8) Practical workflow tips
Start by checking directions: change the sign of q or flip one vector component to confirm the expected reversal. Then refine magnitudes using realistic field values. Finally, download CSV for logs and the PDF for reports, ensuring you can reproduce results while tuning experiments or simulations.
FAQs
1) What units should I use for E and B?
Use N/C (equivalently V/m) for the electric field and tesla (T) for the magnetic field. Keeping SI units ensures the output force is in newtons.
2) Why does the magnetic force disappear sometimes?
The magnetic term is based on v × B. If velocity is parallel or antiparallel to the magnetic field, the cross product is zero, so the magnetic contribution vanishes.
3) How do I know the force direction?
The electric force follows the direction of E for positive charges and reverses for negative charges. The magnetic direction follows the right‑hand rule for v × B, then flips with charge sign.
4) Can I use negative values for components?
Yes. Negative components are expected when vectors point along negative axes. The calculator accepts signed values and scientific notation for compact entry.
5) What does the magnitude |F| tell me?
|F| is the overall strength of the total force vector. It helps compare scenarios quickly, but direction still matters for predicting actual motion and curvature.
6) Are the exports based on my latest inputs?
Yes. CSV and PDF exports recompute using the same submitted inputs. This keeps your downloaded report consistent with the on‑screen results.
7) Why might my result look extremely large or tiny?
Lorentz force scales with charge, field strength, and velocity. Very small particle charges or weak fields can produce tiny forces, while high fields and large charges can create large outputs. Recheck units and exponents.
Professional Article
1) Concept behind the Lorentz force
The Lorentz force describes how electromagnetic fields act on a charge. The total force combines an electric term that accelerates along the field and a magnetic term that bends motion sideways. Three‑axis inputs help you model realistic 3D motion.
2) Why vector components matter
Real field regions rarely align perfectly with one axis. A particle may enter at an angle, and magnets can produce tilted field components. By entering x, y, and z values, you can see how each axis contributes and which direction the net force points.
3) Electric contribution qE
The electric force is Fₑ = qE. It acts even when velocity is zero and is linear in both charge and electric field. In SI, 1 N/C equals 1 V/m. Typical controlled setups range from about 10³ to 10⁵ V/m. Reversing q flips the force direction.
4) Magnetic contribution q(v × B)
The magnetic force is Fₘ = q(v × B) and depends on motion. It is perpendicular to both v and B, so it mainly changes direction rather than speed. Earth’s magnetic field is roughly 25–65 µT, while strong lab systems can reach 1.5–3 T.
5) Interpreting the cross product
The cross product magnitude is |v||B|sinθ, where θ is the angle between velocity and magnetic field. If motion is parallel to the field, θ = 0 and the magnetic term becomes zero. If motion is perpendicular, it is maximized. The calculator outputs v × B so you can verify direction.
6) Typical input scales and unit discipline
Velocities span a wide range: slow drift can be 10²–10⁴ m/s, while electrons in devices can exceed 10⁵ m/s. Keep SI units consistent to avoid scaling errors. Scientific notation is supported, which is useful for small charges such as 1.602e-19 C.
7) Where this model is used
Lorentz force estimates support beam steering, mass spectrometry, Hall‑effect sensing, plasma analysis, and charge‑level intuition for motors and generators. In teaching, it clarifies right‑hand‑rule direction and helps separate what the electric field does versus what the magnetic field does.
8) Reading results and sharing them
After calculating, review component signs, then compare Fₑ and Fₘ magnitudes to see what dominates. If values look wrong, check unit prefixes and whether velocity is parallel to the magnetic field. Use CSV for spreadsheets and PDF for a clean record of inputs and outputs.
FAQs
1) What if my particle is stationary?
If velocity is zero, the magnetic term vanishes because v × B = 0. The calculator returns only the electric contribution, F = qE, with direction set by the sign of the charge and the field direction.
2) Why is the magnetic force sometimes zero?
The magnetic contribution depends on the angle between v and B. If v is parallel or anti‑parallel to B, sinθ = 0 and the cross product is zero. Any perpendicular velocity component restores magnetic force.
3) Can I use V/m instead of N/C for the electric field?
Yes. In SI units, 1 V/m equals 1 N/C. Enter components in either equivalent scale and the computed force will still be in newtons.
4) How do negative charges affect the result?
A negative charge reverses the direction of both electric and magnetic forces compared with a positive charge under the same inputs. Magnitudes remain the same, but vector component signs flip because the force scales linearly with q.
5) What units should I use for B and v?
Use tesla (T) for magnetic field and meters per second (m/s) for velocity. Convert gauss to tesla and km/s to m/s before calculating to avoid unrealistic results.
6) What does the cross product output help me check?
The v × B vector confirms the direction and relative size of the magnetic term. Unexpected values often indicate an angle issue, swapped axes, or a missing unit conversion.
7) When should I download CSV versus PDF?
Use CSV for spreadsheets, batch comparisons, and further calculations. Use PDF when you want a clean, single‑page record for documentation, sharing, or archiving with lab notes.