Enter Charge, Velocity, and Magnetic Field
Use signed Cartesian components. The calculator converts chosen units into SI units before evaluating the magnetic force vector.
Formula Used
F = q(v × B)
Fx = q(vyBz − vzBy)
Fy = q(vzBx − vxBz)
Fz = q(vxBy − vyBx)
The magnitude is |F| = |q||v||B|sin θ. The force is perpendicular to both velocity and magnetic field. A positive charge follows v × B. A negative charge points in the opposite direction.
How to Use This Calculator
- Choose the charge unit and enter its signed value.
- Choose one velocity unit for all three velocity components.
- Enter velocity components using one right-handed coordinate system.
- Choose one magnetic-field unit and enter the three field components.
- Select Calculate Force Direction to display results above the form.
- Review the unit vector and axis angles for the force direction.
Example Data
| Quantity | Value | Interpretation |
|---|---|---|
| Charge, q | +1 µC | Positive test charge |
| Velocity, v | <0, 300, 0> m/s | Points along positive y |
| Magnetic field, B | <0, 0, 0.2> T | Points along positive z |
| Calculated force, F | <6.0 × 10−5, 0, 0> N | Points along positive x |
Understanding Magnetic Force Direction
Magnetic force acts on a moving electric charge. Its direction depends on three things. These are charge sign, velocity direction, and magnetic-field direction. The force never points along the particle path. It also never points along the magnetic field. Instead, it points perpendicular to both vectors. This perpendicular relationship makes magnetic motion different from electric acceleration. A magnetic field can bend a charged particle without changing its speed. It redirects the particle, rather than doing work on it.
Vector Relationships
The cross product supplies the geometric rule. First, orient your right hand from velocity toward magnetic field. Your thumb then identifies the direction for a positive charge. A negative charge feels the opposite direction. This sign reversal is essential for electrons. The calculator evaluates all vector components automatically. It first converts selected units into SI values. It then computes the cross product. Finally, it multiplies every component by the signed charge.
Component entry provides more detail than a simple direction selector. Enter velocity as x, y, and z components. Enter magnetic field in the same coordinate system. The tool reports the force vector in newtons. It also reports the vector magnitude. Direction cosines show how the force aligns with each positive axis. Axis angles give another clear description. These outputs are useful for laboratory work, engineering checks, and vector mechanics exercises.
Interpreting Results
The angle between velocity and field controls magnetic-force size. Perpendicular vectors produce the largest possible force. Parallel or antiparallel vectors produce zero force. A zero result does not always mean an input error. It may correctly describe aligned vectors. Zero charge also gives zero magnetic force. In either case, a unique force direction cannot be assigned. The calculator states this directly to prevent misleading conclusions.
Practical Accuracy
Choose units carefully before calculation. Charge often appears in microcoulombs or elementary charges. Magnetic fields may appear in tesla, millitesla, microtesla, or gauss. Velocity may be stated in metres per second or kilometres per second. Converting every value internally prevents scale mistakes. Review signed component values as well. A minus sign changes vector orientation. It can reverse one or more force components.
Use a consistent right-handed coordinate system. In the usual convention, x cross y points toward positive z. Reversing an axis definition changes reported directions. Keep the same axes for velocity and field inputs. Compare the final vector with a sketch. This quick check catches common transcription errors. For higher confidence, inspect the dot product. The force should be perpendicular to both velocity and magnetic field, except for rounding effects.
Record your inputs with their units when sharing a result. The calculated magnitude alone is incomplete. A force vector needs its sign and axis orientation. Use the component table when comparing experiments or simulations. Small values can be shown in scientific notation. Round only after reviewing the unrounded calculation. This preserves meaningful differences between nearly aligned vectors and exactly parallel vectors during careful technical reporting.
Frequently Asked Questions
What force does this calculator find?
It finds the magnetic force on a moving charged particle. It uses charge, velocity, and magnetic-field vectors. It does not include an electric-field force term.
Why do I enter signed components?
Signs define direction along each coordinate axis. Positive and negative components let the calculator form an accurate cross product and an accurate force direction.
How does charge sign change the result?
A positive charge follows the right-hand-rule cross-product direction. A negative charge experiences the exact opposite force direction. The magnitude remains unchanged for the same absolute charge.
What happens when velocity is parallel to the field?
The cross product becomes zero. Therefore, the magnetic force is zero. The particle can still move, but the magnetic field does not bend its path in that moment.
Can I use gauss for the magnetic field?
Yes. Choose gauss from the field-unit menu. The calculator converts it internally, using 1 gauss = 0.0001 tesla.
What are direction cosines?
They are the x, y, and z components of a unit vector. They show the force direction independently of force magnitude.
Why are F · v and F · B shown?
They verify perpendicularity. For an ideal magnetic force, both dot products are zero. Very small displayed differences usually result from numerical rounding.
Can this calculate an electron force?
Yes. Enter a negative charge value, or enter −1 while using elementary charge units. The calculator reverses the positive-charge force direction automatically.
Does magnetic force change particle speed?
In the ideal magnetic-only model, no. The force remains perpendicular to velocity, so it redirects motion without doing mechanical work on the particle.
Which coordinate system should I use?
Use any right-handed Cartesian system. Keep the same x, y, and z axes for velocity and field values. Consistency is more important than axis labels.
Can I save my result?
After a calculation, use the CSV or PDF button in the result panel. Both downloads contain the displayed vector quantities and directional checks.