22.5 Force on a Moving Charge in a Magnetic Field: Examples and Applications
3 min read•june 18, 2024
Magnetic fields exert forces on moving charged particles, causing them to follow circular or spiral paths. This phenomenon is crucial in various applications, from particle accelerators to mass spectrometers, showcasing the interplay between electricity and magnetism.
Understanding the motion of charged particles in magnetic fields helps explain natural phenomena like auroras and enables technological advancements. The formula provides insights into particle behavior, connecting particle properties with characteristics.
Magnetic Fields and Charged Particle Motion
Motion of charged particles in magnetic fields
Top images from around the web for Motion of charged particles in magnetic fields
11.3 Motion of a Charged Particle in a Magnetic Field – University Physics Volume 2 View original
Is this image relevant?
11.3 Motion of a Charged Particle in a Magnetic Field – University Physics Volume 2 View original
Is this image relevant?
Motion of a Charged Particle in a Magnetic Field | Boundless Physics View original
Is this image relevant?
11.3 Motion of a Charged Particle in a Magnetic Field – University Physics Volume 2 View original
Is this image relevant?
11.3 Motion of a Charged Particle in a Magnetic Field – University Physics Volume 2 View original
Is this image relevant?
1 of 3
Top images from around the web for Motion of charged particles in magnetic fields
11.3 Motion of a Charged Particle in a Magnetic Field – University Physics Volume 2 View original
Is this image relevant?
11.3 Motion of a Charged Particle in a Magnetic Field – University Physics Volume 2 View original
Is this image relevant?
Motion of a Charged Particle in a Magnetic Field | Boundless Physics View original
Is this image relevant?
11.3 Motion of a Charged Particle in a Magnetic Field – University Physics Volume 2 View original
Is this image relevant?
11.3 Motion of a Charged Particle in a Magnetic Field – University Physics Volume 2 View original
Is this image relevant?
1 of 3
- Magnetic fields exert a force on moving charged particles perpendicular to both the particle's velocity and the magnetic field direction ()
- This force causes the to move in a circular or spiral path depending on the angle between the particle's velocity and the magnetic field
- occurs when the particle's velocity is perpendicular to the magnetic field resulting in a constant magnetic force and uniform circular motion (electrons in a )
- The radius of the circular path depends on the particle's charge, mass, velocity, and the strength of the magnetic field (protons in a )
- occurs when the particle's velocity has a component parallel to the magnetic field which remains unaffected while the perpendicular component causes circular motion (electrons in a )
- The pitch of the spiral depends on the ratio of the parallel and perpendicular velocity components relative to the magnetic field direction (alpha particles in a )
- When a charged particle enters a magnetic field at an angle, it follows a
Radius of curvature calculations
- The for a charged particle moving in a magnetic field can be calculated using the formula
- represents the mass of the particle, is the velocity of the particle perpendicular to the magnetic field, is the charge of the particle, and is the magnetic field strength
- The radius of curvature is directly proportional to the particle's mass and velocity meaning heavier particles or those with higher velocities will have larger radii (protons vs electrons)
- The radius of curvature is inversely proportional to the particle's charge and the magnetic field strength so particles with greater charge or in stronger magnetic fields will have smaller radii (alpha particles vs beta particles)
- The radius of curvature is also known as the in plasma physics
Applications of magnetic forces
- Particle accelerators use magnetic fields to guide and accelerate charged particles to high energies by confining them to circular or spiral paths
- Linear accelerators accelerate particles in a straight line using a series of alternating electric fields ()
- Cyclotrons accelerate particles in a spiral path using a constant magnetic field and alternating electric fields (medical production)
- Synchrotrons accelerate particles in a circular path using synchronized magnetic and electric fields ()
- Mass spectrometers use magnetic fields to separate ions based on their by measuring the radii of curvature of the ions' paths
- Ions with different mass-to-charge ratios follow different circular paths in the magnetic field (separating isotopes of uranium)
- The radius of curvature for each ion depends on its mass, charge, and velocity according to the formula
- Applications include identifying chemical compounds (drug testing), analyzing isotopes (carbon dating), and studying molecular structures (protein analysis)
Additional Concepts in Electromagnetic Interactions
- The magnetic force on a moving charge is determined by the of the velocity and magnetic field vectors
- (B) is a measure of the strength and direction of a magnetic field in a given area
- The occurs when a magnetic field applied to a current-carrying conductor creates a voltage difference perpendicular to the current flow
- is the process of generating an electric current in a conductor by varying the magnetic field around it
Key Terms to Review (38)
Cathode Ray Tube: A cathode ray tube (CRT) is a vacuum-sealed glass or metal container that produces images by using a beam of electrons to strike a phosphorescent screen. This technology was widely used in early television sets and computer monitors before the advent of flat-panel displays.
Charged Particle: A charged particle is an atomic or subatomic particle that possesses an electric charge, either positive or negative. These charged particles are fundamental to many physical phenomena, including the behavior of electric and magnetic fields, the motion of charged objects, and the interactions between matter and energy.
Circular Motion: Circular motion is the motion of an object in a circular path or orbit around a central point or axis. This type of motion is characterized by the object continuously changing direction while maintaining a constant distance from the center of the circle.
Cloud Chamber: A cloud chamber is a device used to detect and study the paths of charged particles, such as alpha particles, beta particles, and cosmic rays. It works by creating a supersaturated environment that allows the visualization of these invisible particles as they ionize the surrounding gas, leaving behind a trail of condensed vapor.
Coulomb: Coulomb is the fundamental unit of electric charge, named after the French physicist Charles-Augustin de Coulomb. It is a measure of the amount of electric charge and is a crucial concept in understanding various topics in electricity and magnetism, such as static electricity, electric fields, electric potential, and the behavior of charged particles.
Coulomb force: Coulomb force, also known as the electrostatic force, is the force of attraction or repulsion between two charged particles. It follows an inverse-square law and is governed by Coulomb's law.
Cross Product: The cross product, also known as the vector product, is a binary operation on two vectors that results in a third vector that is perpendicular to both of the original vectors. It is a fundamental concept in physics, particularly in the study of magnetic fields and the forces acting on charged particles within those fields.
Cyclotron: A cyclotron is a type of particle accelerator that uses a combination of a static magnetic field and a rapidly varying electric field to accelerate charged particles in a spiral trajectory. It is used in various applications, including medical therapy and nuclear physics research.
Cyclotron: A cyclotron is a type of particle accelerator that uses a magnetic field and an oscillating electric field to accelerate charged particles, such as protons or ions, in a spiral path. This device is widely used in nuclear physics research and medical applications, such as the production of radioisotopes for medical imaging and cancer treatment.
Electric and magnetic fields: Electric and magnetic fields are two interdependent fields that propagate as waves through space. They form the basis of electromagnetic waves, where oscillations in one field induce oscillations in the other.
Electromagnetic Induction: Electromagnetic induction is the process by which a changing magnetic field induces an electromotive force (EMF) in a conductor, causing an electric current to flow. This phenomenon is the fundamental principle behind the operation of many electrical devices and systems, including transformers, generators, and motors.
Gyroradius: The gyroradius, also known as the Larmor radius, is the radius of the circular path that a charged particle, such as an electron or an ion, follows when it is moving in a magnetic field. This term is particularly relevant in the context of the force on a moving charge in a magnetic field, as the gyroradius is a crucial parameter in understanding the behavior of charged particles under the influence of a magnetic field.
Hall effect: The Hall effect is the production of a voltage difference (the Hall voltage) across an electrical conductor when a magnetic field is applied perpendicular to the current. It demonstrates the nature of charge carriers in a conductor.
Hall Effect: The Hall effect is a phenomenon in which a voltage difference is produced across an electrical conductor transverse to an electric current in the conductor and a magnetic field perpendicular to the current. This effect is widely used in various applications, including magnetic field sensors, current sensors, and Hall-effect switches.
Helical Motion: Helical motion, also known as spiral motion, is a type of motion where an object follows a curved path that wraps around an axis or center point, similar to the shape of a helix or spiral. This motion is often observed in various physical phenomena, including the behavior of charged particles in a magnetic field.
Isotope: Isotopes are atoms of the same element that have the same number of protons in their nucleus but a different number of neutrons. This results in isotopes having the same atomic number but different mass numbers, leading to slight variations in their physical and chemical properties.
Large Hadron Collider: The Large Hadron Collider (LHC) is the world's largest and most powerful particle accelerator, used to study the most fundamental components of matter and the forces that govern them. It plays a crucial role in the fields of particle physics, nuclear physics, and cosmology, connecting various topics in physics, including the force on a moving charge in a magnetic field, relativistic energy, the creation of matter from energy, and the application of high-temperature superconductors.
Linear accelerator: A linear accelerator, or linac, is a device that uses electromagnetic fields to accelerate charged particles to high speeds along a straight path. It is commonly used in particle physics experiments and medical applications.
Linear Accelerator: A linear accelerator is a type of particle accelerator that uses electric and magnetic fields to accelerate charged particles, such as electrons or protons, in a straight line. This technology is widely used in various applications, including medical treatments, scientific research, and industrial processes.
Lorentz force: The Lorentz force is the force experienced by a charged particle moving through an electric and magnetic field. It is given by the equation $\mathbf{F} = q(\mathbf{E} + \mathbf{v} \times \mathbf{B})$, where $q$ is the charge, $\mathbf{E}$ is the electric field, $\mathbf{v}$ is the velocity of the particle, and $\mathbf{B}$ is the magnetic field.
Lorentz Force: The Lorentz force is the force exerted on a moving charged particle when it is placed in a magnetic field. It is a fundamental concept in electromagnetism that describes the interaction between electric and magnetic fields and the motion of charged particles.
Magnetic Bottle: A magnetic bottle is a configuration of magnetic fields that can be used to confine charged particles, such as plasma or charged particles in a fusion reactor. It is created by the interaction between a strong magnetic field and the motion of the charged particles, which are forced to follow the magnetic field lines.
Magnetic Field: A magnetic field is a region in space where magnetic forces can be detected. It is a vector field that describes the magnetic influence of electric currents and magnetized materials on the space around them. The magnetic field is a fundamental concept in electromagnetism and is essential for understanding various phenomena in physics, including the behavior of ferromagnets, the motion of charged particles, and the production of electromagnetic waves.
Magnetic Flux Density: Magnetic flux density, also known as magnetic induction or magnetic field strength, is a measure of the strength of a magnetic field. It quantifies the amount of magnetic flux per unit area perpendicular to the direction of the field. This term is crucial in understanding various electromagnetic phenomena, including the force on a moving charge, the Hall effect, the magnetic force between parallel conductors, motional electromotive force (emf), and eddy currents.
Mass Spectrometer: A mass spectrometer is an analytical instrument used to identify the chemical composition and structure of a sample by ionizing the sample and separating the resulting ions based on their mass-to-charge ratio. It is a powerful tool for studying the force on a moving charge in a magnetic field, which is a key concept in the context of 22.5 Force on a Moving Charge in a Magnetic Field: Examples and Applications.
Mass-to-Charge Ratio: The mass-to-charge ratio, often denoted as m/q or m/e, is a fundamental physical quantity that describes the ratio of the mass of a particle to its electric charge. This ratio is an important parameter in the study of charged particles, particularly in the context of their motion and behavior in electric and magnetic fields.
Particle Accelerator: A particle accelerator is a device that uses electromagnetic fields to propel charged particles, such as electrons, protons, or ions, to high speeds and energies. These accelerated particles are then used for various applications, including scientific research, medical treatments, and industrial processes.
R = mv/qB: The term 'r = mv/qB' represents the radius of the circular path that a charged particle will follow when moving through a magnetic field. This equation describes the relationship between the particle's momentum, charge, and the strength of the magnetic field, which determines the curvature of the particle's trajectory.
Radius of curvature: The radius of curvature is the distance from the center of a circular path to any point on the path. It is used to describe the size of the circle in uniform circular motion.
Radius of Curvature: The radius of curvature is a measure of the curvature of a curve or surface at a specific point. It represents the radius of the circular arc that best approximates the curve or surface at that point. This concept is particularly important in the study of mechanics, optics, and other physical phenomena.
Right-hand rule: The right-hand rule is a mnemonic used to determine the direction of angular momentum vectors. It states that if you curl the fingers of your right hand in the direction of rotation, your thumb points in the direction of the angular momentum vector.
Right-Hand Rule: The right-hand rule is a mnemonic device used to determine the direction of various vector quantities in physics, such as magnetic fields, angular momentum, and the force on a moving charge in a magnetic field. It is a simple and intuitive way to visualize the relationship between these vectors and their associated directions.
SLAC: SLAC, which stands for Stanford Linear Accelerator Center, is a renowned particle accelerator facility that has made significant contributions to the field of high-energy physics. It is a linear accelerator that is used to accelerate charged particles, such as electrons and positrons, to extremely high energies, enabling researchers to study the fundamental building blocks of matter and the forces that govern their interactions.
Spiral Motion: Spiral motion refers to the circular or helical path taken by a charged particle when it experiences a force in a magnetic field. This motion is a result of the interaction between the magnetic force and the velocity of the charged particle, leading to a circular trajectory around the magnetic field lines.
Synchrotron: A synchrotron is a type of particle accelerator that uses magnetic fields to accelerate charged particles in a circular path. It is instrumental in high-energy physics experiments and the creation of new particles.
Synchrotron: A synchrotron is a type of particle accelerator that uses a magnetic field to accelerate charged particles, such as electrons or protons, to extremely high energies. It is a crucial device in the field of particle physics, enabling the study of fundamental particles and their interactions.
Tesla: The tesla (T) is the SI unit of magnetic field strength or magnetic flux density. It measures how much force a magnetic field exerts on moving charges or current-carrying wires.
Tesla: The tesla (T) is the unit of magnetic flux density or magnetic induction in the International System of Units (SI). It is named after the Serbian-American inventor and electrical engineer Nikola Tesla, who made significant contributions to the design of the modern alternating-current (AC) electrical supply system.