Lorentz Force Calculator
Calculate magnetic Lorentz force on a moving charged particle or a current-carrying wire. View SI conversions, every solution step, and a live direction-and-value diagram.
Lorentz Force Diagram and Values
The three perpendicular arrows make force direction and every calculation value easy to read.
Step-by-Step Solution
Here's exactly how this answer was calculated, one step at a time.
Given: q = 2 µC, v = 3,000,000 m/s, B = 50 mT, θ = 90°
Step 1: Convert to SI units
q = 2 µC = 0.000002 C; B = 50 mT = 0.05 TStep 2: Write the magnetic force formula
Only the component perpendicular to the magnetic field produces force.
F = qvB sin θStep 3: Substitute known values
F = 0.000002 × 3,000,000 × 0.05 × sin(90°)Step 4: Calculate force magnitude
F = 0.3 N
The magnetic force magnitude is:
0.3 N
Free Lorentz Force Calculator
This Lorentz Force Calculator finds the magnetic force on a moving charged particle or a current-carrying conductor. Choose the model, add your values, and the result updates with correct SI unit conversion. The page displays the Lorentz force formula, substitution, final force in newtons, perpendicular component, and a colour-coded vector diagram. It is ideal for electromagnetism homework, classroom examples, motors, particle physics and basic circuit physics.
A magnetic force exists only when charge moves through a magnetic field with a perpendicular component. The angle control matters: at 90 degrees the force is maximum, while at zero degrees the force is zero. This calculator gives magnitude; use the right-hand rule and the charge sign to determine the physical direction.
Lorentz Force Formula
For a particle, magnetic Lorentz force magnitude is F = qvB sin θ. F is force in newtons, q is charge in coulombs, v is speed in metres per second, B is magnetic flux density in tesla, and θ is the angle between velocity and field. A microcoulomb must be converted to coulombs and millitesla to tesla before calculation.
For a straight current-carrying wire, the equivalent force equation is F = BIL sin θ. I is current in amperes and L is the active wire length in metres. A wire contains many moving charges, so this is the large-scale version of the same magnetic interaction.
Lorentz Force Worked Example
Suppose a particle has charge 2 µC, velocity 3,000,000 m/s and crosses a 50 mT magnetic field at 90 degrees. Convert q = 2 × 10⁻⁶ C and B = 0.050 T. Then F = qvB sin 90° = 2 × 10⁻⁶ × 3,000,000 × 0.050 × 1 = 0.3 N.
If the angle becomes 30 degrees, sin 30° is 0.5, so the force becomes 0.15 N. This shows why only perpendicular motion matters. Parallel motion has sin 0° = 0 and therefore feels no magnetic force, even in a strong field.
Direction: Right-Hand Rule
For a positive charge, point the fingers of your right hand along velocity and curl them toward the magnetic field. Your thumb gives force direction. For a negative electron, reverse the answer. In the visual diagram, velocity points right, field points into the page, and force points upward for a positive charge.
This directional rule is essential in mass spectrometers, velocity selectors, motors and charged-particle beams. Magnetic force is always perpendicular to the velocity, so it changes direction of motion rather than doing work or changing speed by itself.
Applications and Practical Notes
Lorentz force explains how electric motors create torque, how speakers move a coil, and why moving charges curve in magnetic fields. In a uniform field perpendicular to velocity, a particle follows circular motion. The radius is r = mv/(qB), where m is mass.
Use ideal values for study, but real systems may have non-uniform fields, changing direction, relativistic speeds or mechanical constraints. Keep strong magnets away from sensitive equipment and follow electrical safety practices around high-current conductors.
Frequently Asked Questions
What is the Lorentz force formula?
For a moving charge, F = qvB sin θ. For a straight current-carrying wire, F = BIL sin θ.
Why is Lorentz force zero at 0 degrees?
The formula contains sin θ. Since sin 0° is zero, motion parallel to magnetic field lines has no magnetic force.
What is the SI unit of Lorentz force?
The SI unit is the newton (N). Use charge in coulombs, field in tesla, velocity in m/s and length in metres.
Does a magnetic field change particle speed?
An ideal magnetic force is perpendicular to velocity, so it bends the path but does not change speed or kinetic energy.
How does a negative charge change direction?
Its force direction is opposite to the right-hand-rule result for a positive charge.
When is force maximum?
At 90 degrees to the field because sin 90° = 1.