Magnetic Force Calculator
Calculate the magnetic (Lorentz) force on a moving charge using F = qvB (assuming perpendicular motion, sin θ = 1). Supports unit conversions for charge, velocity, magnetic field, and force.
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What is Magnetic Force?
Magnetic force is the force exerted by a magnetic field on a moving charged particle. It is one component of the Lorentz force, which describes the total electromagnetic force on a charge. The magnetic force is always perpendicular to both the particle’s velocity and the magnetic field direction:
F = qvB sin θ
Where F is force in newtons (N), q is charge in coulombs (C), v is velocity in meters per second (m/s), B is magnetic flux density in teslas (T), and θ is the angle between v and B. This calculator assumes sin θ = 1 (perpendicular motion) for maximum force.
Common Magnetic Field Strengths
| Source | Field (T) |
|---|---|
| Earth’s magnetic field (surface) | 0 |
| Neodymium magnet (surface) | 1.25 |
| MRI machine (typical) | 1.5 |
| Fridge magnet | 0.005 |
| Sunspot magnetic field | 0.3 |
| Interstellar magnetic field | 0 |
| Electromagnet (lab) | 2 |
| Strongest pulsed magnet (lab) | 100 |
Related Calculators
Authoritative References
Frequently Asked Questions
What is magnetic force?
Magnetic force is the force exerted on a moving charged particle in a magnetic field. It is given by the Lorentz force law: F = qvBsin(θ), where q is charge, v is velocity, B is magnetic field strength, and θ is the angle between velocity and field directions.
What is the Lorentz force?
The Lorentz force is the total electromagnetic force on a charged particle: F = q(E + v × B). The magnetic component F = q(v × B) is always perpendicular to both velocity and magnetic field, causing circular or helical motion.
What happens to a charge moving perpendicular to a magnetic field?
When a charged particle moves perpendicular to a uniform magnetic field, it experiences a centripetal force that causes it to move in a circular path. The radius is r = mv/(qB), and the frequency is called the cyclotron frequency.
How does the angle between velocity and magnetic field affect force?
The magnetic force depends on sin(θ). At θ = 90° (perpendicular), force is maximum. At θ = 0° or 180° (parallel or antiparallel), force is zero. At other angles, only the perpendicular component of velocity contributes.
What direction does magnetic force act?
Magnetic force acts perpendicular to both the velocity vector and the magnetic field vector, following the right-hand rule. For a positive charge, point thumb in velocity direction, fingers in field direction, and the palm pushes in the force direction.
What is a tesla (T)?
One tesla is the magnetic field strength that exerts one newton of force on a one-coulomb charge moving at one meter per second perpendicular to the field. 1 T = 1 N/(A·m). Earth’s magnetic field is about 25–65 μT.
What is a gauss (G)?
The gauss is a CGS unit of magnetic flux density. 1 G = 10⁻⁴ T = 100 μT. Earth’s magnetic field is about 0.25–0.65 G. A typical fridge magnet is about 50 G (5 mT).
How is magnetic force used in particle accelerators?
Particle accelerators use powerful magnetic fields to steer and focus charged particle beams. The Lorentz force bends particles into curved paths. The LHC uses 8.3 T superconducting magnets to keep protons in a 27 km circular path.
What is an elementary charge?
The elementary charge e = 1.602176634 × 10⁻¹⁹ C is the smallest unit of electric charge commonly encountered. Protons have charge +e and electrons have charge –e. All observable charges are integer multiples of e.
How does magnetic force differ from electric force?
Electric force acts on stationary charges and is parallel to the electric field. Magnetic force acts only on moving charges and is perpendicular to both velocity and magnetic field. Electric force can do work; magnetic force cannot (it is always perpendicular to displacement).
Can magnetic force speed up a particle?
No, magnetic force cannot change a particle’s speed because it always acts perpendicular to velocity. It only changes the direction of motion, resulting in centripetal acceleration without changing kinetic energy.
What is the right-hand rule?
The right-hand rule determines the direction of magnetic force on a positive charge: point thumb in velocity direction, fingers in magnetic field direction, and the force direction is out of the palm. For negative charges, reverse the direction.
What is the cyclotron frequency?
Cyclotron frequency is the frequency at which a charged particle orbits in a uniform magnetic field: f = qB/(2πm). It depends only on charge, magnetic field, and mass — not on velocity. This principle is used in cyclotron accelerators and mass spectrometers.
How do mass spectrometers use magnetic force?
Mass spectrometers use magnetic fields to deflect ions by their mass-to-charge ratio. Ions moving through a magnetic field follow circular paths with radius r = mv/(qB). Heavier ions have larger radii, allowing separation and identification.
What is the Hall effect?
The Hall effect occurs when a current-carrying conductor is placed in a perpendicular magnetic field. The Lorentz force deflects charge carriers to one side, creating a transverse voltage (Hall voltage) proportional to the magnetic field strength.
How is magnetic force used in electric motors?
Electric motors use the Lorentz force on current-carrying wires in a magnetic field. The force F = I(L × B) on each wire segment produces torque that rotates the motor shaft. The direction of current is switched periodically to maintain rotation.
What is magnetic force on a current-carrying wire?
A current-carrying wire in a magnetic field experiences force F = ILB sin(θ), where I is current, L is wire length, and θ is the angle between wire and field. This is the principle behind electric motors and speakers.
What is the difference between magnetic field B and H?
B (magnetic flux density or magnetic induction) is the total field including material response. H (magnetic field strength) excludes magnetization. In vacuum, B = μ₀H. In materials, B = μ₀(H + M) where M is magnetization.
What materials are affected by magnetic fields?
Ferromagnetic materials (iron, nickel, cobalt, gadolinium) are strongly attracted to magnetic fields. Paramagnetic materials (aluminum, platinum) are weakly attracted. Diamagnetic materials (copper, bismuth, water) are weakly repelled.
What is magnetic levitation?
Magnetic levitation (maglev) uses magnetic force to suspend objects without physical contact. Maglev trains use electromagnets to lift and propel the train. The Lorentz force on superconducting magnets provides stable levitation with zero friction.
How strong is Earth’s magnetic field?
Earth’s magnetic field at the surface ranges from about 25 μT (0.25 G) near the equator to 65 μT (0.65 G) near the poles. It protects the planet from solar wind and cosmic radiation by deflecting charged particles.
What is the magnetic field inside an MRI machine?
Clinical MRI machines use 1.5 T or 3 T superconducting magnets. Research MRI systems reach up to 11.7 T. These strong fields align hydrogen nuclei in the body, enabling detailed medical imaging through nuclear magnetic resonance.
What is a neodymium magnet?
Neodymium magnets (NdFeB) are the strongest permanent magnets, with surface fields up to 1.4 T. They are made from neodymium, iron, and boron. They are used in hard drives, headphones, motors, and magnetic resonance imaging.
Can magnetic fields affect human health?
Static magnetic fields like those from MRI machines are generally considered safe. Strong fields above 2 T can cause vertigo, nausea, and metallic taste. The World Health Organization classifies static magnetic fields as possibly carcinogenic (Group 2B).
Can a magnetic field block radiation?
Magnetic fields can deflect charged particles (alpha and beta radiation, cosmic rays) but do not block uncharged radiation (gamma rays, X-rays, neutrons). This is why Earth’s magnetic field protects us from solar wind but not from gamma rays.
What is the Zeeman effect?
The Zeeman effect is the splitting of spectral lines when atoms are placed in a magnetic field. It occurs because the magnetic field interacts with the magnetic moment of electrons, shifting their energy levels. It is used in astronomy to measure stellar magnetic fields.
What is magnetic confinement fusion?
Magnetic confinement fusion uses strong magnetic fields to confine hot plasma for nuclear fusion. Tokamaks (like ITER) use toroidal magnetic fields to keep the plasma away from walls, enabling fusion reactions at temperatures over 100 million °C.
What is the relationship between electricity and magnetism?
Electricity and magnetism are unified in electromagnetism. A changing electric field creates a magnetic field (Ampère’s law), and a changing magnetic field creates an electric field (Faraday’s law). Maxwell’s equations describe this unified framework.
What happens to a charge at rest in a magnetic field?
A stationary charged particle experiences no magnetic force because magnetic force requires motion. Only electric fields exert force on stationary charges. The Lorentz force term q(v × B) vanishes when v = 0.
What is the magnetoresistance effect?
Magnetoresistance is the change in electrical resistance when a material is exposed to a magnetic field. It occurs because the Lorentz force deflects charge carriers, altering their path length. Giant magnetoresistance (GMR) is used in read heads of hard drives.