Lorentz Force
The Lorentz force F = q(E + v ร B) is the total force on a charged particle in electric and magnetic fields. Electric force qE is along E; magnetic force q(v ร B) is perpendicular to both v and B, causing circular or helical motion.
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Magnetic force is perpendicular to velocity; it changes direction, not speed. Cyclotron radius r = mv/(qB) separates ions by mass in spectrometers. Velocity selector: v = E/B when electric and magnetic forces balance. Hall voltage V_H = vBd from deflection of charge carriers.
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Why: Lorentz force underlies mass spectrometers, particle accelerators, Hall effect sensors, CRTs, and cyclotrons. It explains charged particle motion in plasmas and magnetic confinement.
How: Electric force accelerates along E. Magnetic force does no work (perpendicular to v) but deflects; perpendicular v and B yield circular motion. Combined E and B give cycloid trajectories.
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๐ฌ Mass Spectrometer
Ion separation in mass spectrometer: q=1.6ร10โปยนโน C, B=0.5 T, v=10โถ m/s
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โก Hall Effect Sensor
Hall effect in semiconductor: q=-1.6ร10โปยนโน C, B=0.1 T, v=10โต m/s, d=1 mm
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๐ Particle Accelerator
Particle in accelerator: q=1.6ร10โปยนโน C, E=10โถ V/m, B=1 T, v=10โท m/s
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๐ฏ Velocity Selector
Velocity selector: E=10โด V/m, B=0.01 T, perpendicular fields
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๐บ Electron Beam Deflection
Electron beam in CRT: q=-1.6ร10โปยนโน C, B=0.001 T, v=10โท m/s
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๐ Cyclotron Motion
Charged particle in cyclotron: q=1.6ร10โปยนโน C, B=2 T, v=10โถ m/s, m=1.67ร10โปยฒโท kg
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Enter Parameters
For educational and informational purposes only. Verify with a qualified professional.
๐ฌ Physics Facts
Magnetic force does zero work on charged particles; it only deflects.
โ Griffiths
Mass spectrometers use r = mv/(qB) to separate ions by mass-to-charge ratio.
โ Analytical chemistry
Hall effect sensors measure B by detecting transverse voltage in conductors.
โ Solid-state physics
Cyclotron frequency f = qB/(2ฯm) is independent of particle speed.
โ Particle accelerators
What is the Lorentz Force?
The Lorentz force is the combined force experienced by a charged particle moving through both electric and magnetic fields. It is fundamental to understanding particle motion in electromagnetism and forms the basis for many practical applications including mass spectrometers, particle accelerators, and Hall effect sensors.
Electric Force
F_E = qE acts in the direction of the electric field for positive charges, independent of velocity.
Magnetic Force
F_B = q(v ร B) is perpendicular to both velocity and magnetic field, causing circular or helical motion.
Combined Force
F = q(E + v ร B) combines both forces, resulting in complex trajectories including cycloid motion.
How Does the Lorentz Force Work?
The Lorentz force calculation involves vector mathematics to determine the combined effect of electric and magnetic fields on charged particles. The calculator uses cross products, vector addition, and circular motion physics to provide comprehensive analysis.
๐ฌ Calculation Process
- 1Convert all inputs to SI units (Coulombs, Tesla, m/s, kg)
- 2Calculate electric force: F_E = qE (vector multiplication)
- 3Calculate magnetic force: F_B = q(v ร B) using cross product
- 4Add forces vectorially: F_total = F_E + F_B
- 5Calculate cyclotron radius and frequency for circular motion
When to Use Lorentz Force Calculations
Lorentz force calculations are essential in particle physics, electromagnetism research, and numerous practical applications involving charged particle motion.
๐ฌ Mass Spectrometry
Separate ions by mass-to-charge ratio using magnetic field deflection. Essential for chemical analysis and isotope separation.
โก Hall Effect Sensors
Measure magnetic fields and current in semiconductors. Used in position sensors, current sensors, and magnetic field measurement.
๐ Particle Accelerators
Control and focus particle beams using combined electric and magnetic fields. Critical for particle physics research.
Lorentz Force Formulas
Lorentz Force
Total force combining electric and magnetic components
Cyclotron Radius
Radius of circular motion in uniform magnetic field
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