Lorentz Force - Revision history

SrihithaJagarlamudi: /* Applications */

2025-12-01T03:54:26Z

Applications

← Older revision		Revision as of 23:54, 30 November 2025
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	Scientists at the European Organization for Nuclear Research(CERN), the largest organization for particle research, take advantage of the Lorentz force in their collider experiments[4].		Scientists at the European Organization for Nuclear Research(CERN), the largest organization for particle research, take advantage of the Lorentz force in their collider experiments[4].

			Furthermore, Mass spectrometers rely on the Lorentz force in order to separate charged particles based on the ratio of mass and charge. When ions are generated, the electric field accelerates them to gain kinetic energy. When the ions enter a perpendicular magnetic field, the Lorentz force magnetic component will cause them to follow a more curved trajectory.

			Mass spectrometry is an application that is quite important in various fields such as chemistry and environmental science, as well as for identifying compounds that may be unknown, analyzing structures, etc. Without the Lorentz force, the accuracy would not be possible, making it vital in numerous scientific fields.

	==History==		==History==

SrihithaJagarlamudi at 03:49, 1 December 2025

2025-12-01T03:49:31Z

← Older revision		Revision as of 23:49, 30 November 2025
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	A charged particle experiences an electric force of <50, -120, 80> N and a magnetic force of <-30, 60, -40) N. Find the Lorentz Force.		A charged particle experiences an electric force of <50, -120, 80> N and a magnetic force of <-30, 60, -40) N. Find the Lorentz Force.

	Solution: <50, -120, 80> + <-30, 60, -40> = <20, -60, 40> N		'''Solution: <50, -120, 80> + <-30, 60, -40> = <20, -60, 40> N'''


	The electric force on a certain particle is <100,-600,300> N and the magnetic force is <-600,400,0> N. Find the Lorentz force.		The electric force on a certain particle is <100,-600,300> N and the magnetic force is <-600,400,0> N. Find the Lorentz force.

SrihithaJagarlamudi at 03:48, 1 December 2025

2025-12-01T03:48:50Z

← Older revision		Revision as of 23:48, 30 November 2025
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	[[File:Lorentzdiagram.png]]		[[File:Lorentzdiagram.png]]

	Initially, a negatively charged particle is traveling with initial velocity in the -z direction. There is a constant electric field ''E'' in the -x direction and a constant magnetic field ''B'' in the +y direction. The magnetic force on the negatively charged particle is equal to <math> q\vec{v} ⨯ \vec{B}</math>, or the charge of the particle times the cross product of the particle’s velocity and the magnetic field it travels through. The electric force on the particle is equal to <math> q\vec{E} </math>, or the charge of the particle times the electric field that the particle travels through. Since the magnetic force on the particle is related to the particle’s velocity ''v'', the magnetic force changes as the the particle’s velocity changes. Conversely, the electric force on the particle is constant. Since the Magnetic force is variable, the Lorentz Force on the particle, or the net force due to magnetic and electric forces on the particle (<math> \vec{F}_{Lorentz} = q\vec{E} + q\vec{v} ⨯ \vec{B}</math>) is also variable, and the particle's velocity changes.		Initially, a negatively charged particle is traveling with initial velocity in the -z direction. There is a constant electric field ''E'' in the -x direction and a constant magnetic field ''B'' in the +y direction. The magnetic force on the negatively charged particle is equal to <math> q\vec{v} ⨯ \vec{B}</math>, or the charge of the particle times the cross product of the particle’s velocity and the magnetic field it travels through. The electric force on the particle is equal to <math> q\vec{E} </math>, or the charge of the particle times the electric field that the particle travels through. Since the magnetic force on the particle is related to the particle’s velocity ''v'', the magnetic force changes as the the particle’s velocity changes. Conversely, the electric force on the particle is constant. Since the Magnetic force is variable, the Lorentz Force on the particle, or the net force due to magnetic and electric forces on the particle (<math> \vec{F}_{Lorentz} = q\vec{E} + q\vec{v} ⨯ \vec{B}</math>) is also variable, and the particle's velocity changes.Over time, the interaction between the electric and magnetic forces will produce a sideways drift of the charged particles.

	==Example Problems==		==Example Problems==

	===Simple===		===Simple===

			A charged particle experiences an electric force of <50, -120, 80> N and a magnetic force of <-30, 60, -40) N. Find the Lorentz Force.

			Solution: <50, -120, 80> + <-30, 60, -40> = <20, -60, 40> N

	The electric force on a certain particle is <100,-600,300> N and the magnetic force is <-600,400,0> N. Find the Lorentz force.		The electric force on a certain particle is <100,-600,300> N and the magnetic force is <-600,400,0> N. Find the Lorentz force.

SrihithaJagarlamudi: /* Significance */

2025-12-01T03:43:24Z

Significance

← Older revision		Revision as of 23:43, 30 November 2025
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	This law is central to understanding:		This law is central to understanding:

	Particle motion in fields		Particle motion in fields: Determining the trajectories of electrons, ions, etc.

	Magnetic field generation from currents		Magnetic field generation from currents, and explaining why currents exert forces on each other.

	Applications such as electromagnets and transformers		Applications such as electromagnets and transformers: Many devices rely on the Lorentz force, such as mass spectrometers, Hall Effect sensors, etc.

	However, it does not fully describe collective particle behavior in materials, which requires more complex models like transport equations.		However, it does not fully describe collective particle behavior in materials, which requires more complex models like transport equations. Though the Lorentz force has quite a range of usefulness, the law describes only the behavior of individual particles. When looking at more complex figures or larger groups of charged particles, other forces will also need to be considered.

			Overall, the Lorentz force has connections between electromagnetic theory and the motion of matter, which makes it a very significant law in physics.

	==A Mathematical Model==		==A Mathematical Model==

SrihithaJagarlamudi at 03:37, 1 December 2025

2025-12-01T03:37:20Z

← Older revision		Revision as of 23:37, 30 November 2025
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	[[File:Headerlorentz.png\|400px\|thumb\|right\|Lorentz force diagram]]		[[File:Headerlorentz.png\|400px\|thumb\|right\|Lorentz force diagram]]
	'''Claimed by ~~Xinyan Jiang~~, ~~Spring~~ 2025'''		'''Claimed by Srihitha Jagarlamudi, Fall 2025'''
	== Introduction ==		== Introduction ==

	The Lorentz force is a fundamental concept in electromagnetism, describing the force experienced by a charged particle moving through electric and magnetic fields. It is important in understanding the behavior of particles in various physical systems.		The Lorentz force is a fundamental concept in electromagnetism, describing the force experienced by a charged particle moving through electric and magnetic fields. It is important in understanding the behavior of particles in various physical systems.

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	* <math> \vec{B} </math> is the magnetic field.		* <math> \vec{B} </math> is the magnetic field.

	This equation shows how electric fields exert forces in the direction of the field, while magnetic fields exert forces perpendicular to both the particle’s motion and the magnetic field lines. The Lorentz force not only underpins the operation of electric motors, generators, and particle accelerators, but also provides a framework for deeper exploration of classical and modern physics.		This equation shows how electric fields exert forces in the direction of the field, while magnetic fields exert forces perpendicular to both the particle’s motion and the magnetic field lines. The relationship explains why electric fields can either slow down or sped up particles. The Lorentz force not only underpins the operation of electric motors, generators, and particle accelerators, but also provides a framework for deeper exploration of classical and modern physics.

Zeynepuzun: Undo revision 47436 by Zeynepuzun (talk)

2025-11-30T21:26:47Z

Undo revision 47436 by Zeynepuzun (talk)

← Older revision		Revision as of 17:26, 30 November 2025
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	[[File:Headerlorentz.png\|400px\|thumb\|right\|Lorentz force diagram]]		[[File:Headerlorentz.png\|400px\|thumb\|right\|Lorentz force diagram]]
	'''Claimed by ~~Zeynep Uzun~~, ~~Fall~~ 2025'''		'''Claimed by Xinyan Jiang, Spring 2025'''
	== Introduction ==		== Introduction ==
	The Lorentz force is a fundamental concept in electromagnetism, describing the force experienced by a charged particle moving through electric and magnetic fields. It is important in understanding the behavior of particles in various physical systems.		The Lorentz force is a fundamental concept in electromagnetism, describing the force experienced by a charged particle moving through electric and magnetic fields. It is important in understanding the behavior of particles in various physical systems.

Zeynepuzun at 20:55, 30 November 2025

2025-11-30T20:55:03Z

← Older revision		Revision as of 16:55, 30 November 2025
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	[[File:Headerlorentz.png\|400px\|thumb\|right\|Lorentz force diagram]]		[[File:Headerlorentz.png\|400px\|thumb\|right\|Lorentz force diagram]]
	'''Claimed by ~~Xinyan Jiang~~, ~~Spring~~ 2025'''		'''Claimed by Zeynep Uzun, Fall 2025'''
	== Introduction ==		== Introduction ==
	The Lorentz force is a fundamental concept in electromagnetism, describing the force experienced by a charged particle moving through electric and magnetic fields. It is important in understanding the behavior of particles in various physical systems.		The Lorentz force is a fundamental concept in electromagnetism, describing the force experienced by a charged particle moving through electric and magnetic fields. It is important in understanding the behavior of particles in various physical systems.

Xjiang375 at 23:12, 12 April 2025

2025-04-12T23:12:37Z

← Older revision		Revision as of 19:12, 12 April 2025
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	==Significance==		==Significance==
	The Lorentz force ~~completes the picture that Maxwell's equations paint.~~ Maxwell's equations describe how charged particles and electrical currents or even moving charged particles create and contribute to electric and magnetic fields. The Lorentz force takes Maxwell's equations and completes the picture by describing the force ~~that acts~~ on a ~~moving charge ''q''~~ in ~~the presence of an~~ electromagnetic ~~field(~~s). Lorentz ~~law plays a major role in the behavior of charged~~ particles. ~~One~~ is ~~how the particle itself responds~~ to ~~being subject to Lorentz law. Two is how the electric ''E'' and magnetic ''B''~~ fields by currents and ~~charges are generated~~.		The Lorentz force complements Maxwell's equations by describing the force on a charged particle in electromagnetic fields. While Maxwell's equations define how fields are generated, the Lorentz force explains how particles respond to those fields.

			This law is central to understanding:

			Particle motion in fields

			Magnetic field generation from currents

			Applications such as electromagnets and transformers

			However, it does not fully describe collective particle behavior in materials, which requires more complex models like transport equations.

	Generally, the Lorentz force falls short of being the general solution and cannot describe the collective behavior of charged particles conceptually or mathematically. In materials, one must use more complex transport equations to determine how charges respond within the space they are inhabiting.

	==A Mathematical Model==		==A Mathematical Model==
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	<math> \vec{F}_{Lorentz} = q\vec{E} + q\vec{v} ⨯ \vec{B}</math>		<math> \vec{F}_{Lorentz} = q\vec{E} + q\vec{v} ⨯ \vec{B}</math>

	where '''<math>q\vec{E}</math>''' is the electric force contributed by an external electric field and ''' <math>q\vec{v} ⨯ \vec{B}</math>''' is the magnetic force contributed by an external magnetic field. As many applications involve vectors, it is valuable to recognize the resulting directions of '''<math>q\vec{E}</math>''' and ''' <math>q\vec{v} ⨯ \vec{B}</math>''' in relation to the particle's charge and velocity within the environment of applied electric/magnetic fields. The resulting electric force vector will always be towards or opposite to the applied electric field, depending on the sign of the charge. For example, an electron ~~undergoing~~ an electric field in the +x direction will ~~receive an electric force~~ in the -x direction. The magnetic force on the particle, however, has a direction perpendicular to both the velocity ''v'' of the particle and the magnetic field ''B'', and has a value proportional to ''q'' and to the magnitude of the vector cross product ''' <math>q\vec{v} ⨯ \vec{B}</math>'''. More specifically, the magnitude of the magnetic force equals ''qvBsinθ'' where ''θ'' is the angle between ''v'' and ''B''.		where '''<math>q\vec{E}</math>''' is the electric force contributed by an external electric field and ''' <math>q\vec{v} ⨯ \vec{B}</math>''' is the magnetic force contributed by an external magnetic field. As many applications involve vectors, it is valuable to recognize the resulting directions of '''<math>q\vec{E}</math>''' and ''' <math>q\vec{v} ⨯ \vec{B}</math>''' in relation to the particle's charge and velocity within the environment of applied electric/magnetic fields. The resulting electric force vector will always be towards or opposite to the applied electric field, depending on the sign of the charge. For example, if an electron is in an electric field along the +x direction, the force will point in the -x direction. The magnetic force is always perpendicular to both the direction of motion and the field. The magnetic force on the particle, however, has a direction perpendicular to both the velocity ''v'' of the particle and the magnetic field ''B'', and has a value proportional to ''q'' and to the magnitude of the vector cross product ''' <math>q\vec{v} ⨯ \vec{B}</math>'''. More specifically, the magnitude of the magnetic force equals ''qvBsinθ'' where ''θ'' is the angle between ''v'' and ''B''.

	====Motion of a Charged Particle in a Uniform Magnetic Field====		====Motion of a Charged Particle in a Uniform Magnetic Field====
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	==Applications==		==Applications==

			Cyclotrons and particle accelerators exploit the Lorentz force to guide and accelerate particles. When \vec{v} is perpendicular to \vec{B}, particles orbit in circles and gain energy through electric fields.

			Used in:

			Particle physics (e.g., CERN experiments)

			Radiation therapy

			Mass spectrometry

			More:
	Specific applications of the Lorentz force have enabled some of the most significant scientific experimentation to date.		Specific applications of the Lorentz force have enabled some of the most significant scientific experimentation to date.

Xjiang375 at 22:57, 12 April 2025

2025-04-12T22:57:58Z

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	examples:		examples:

	[[File:~~Two currents in the same direction~~.jpeg\|400px\|center\|thumb\|same direction currents]]		[[File:Two_currents_in _the_same_direction.jpeg\|400px\|center\|thumb\|same direction currents]]

	==Significance==		==Significance==

Xjiang375 at 22:57, 12 April 2025

2025-04-12T22:57:33Z

← Older revision		Revision as of 18:57, 12 April 2025
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	examples:		examples:

	[[File:~~two_current_in_the_same_direction~~\|400px\|center\|thumb\|same direction currents]]		[[File:Two currents in the same direction.jpeg\|400px\|center\|thumb\|same direction currents]]

	==Significance==		==Significance==