Name: charged particle paths in magnetic fields
Uploaded: 2023-04-30T12:40:48.000Z
Duration: 1 min 22 s
Channel: JoVE

K12 Standards

north-carolina-k-12-science-standard-course-of-study

North Carolina K-12 Science Standard Course of Study

9-12

Physical Science

motion-and-stability-forces-and-interactions

Motion and Stability- Forces and Interactions

PS.PSc.6.4

motion-of-a-charged-particle-in-a-magnetic-field

Motion Of A Charged Particle In A Magnetic Field

Düzgün bir manyetik alan B'ye dik olarak hareket eden Q yükünün m nokta kütlesini düşünün.
Lorentz kuvvetinin büyüklüğü sabittir ve her zaman hızına diktir. Yani hızın büyüklüğünü değiştiremez, sadece yönünü değiştirir. Bu nedenle, parçacığın yolu r yarıçaplı bir dairedir.
Newton'un ikinci hareket yasasını kullanarak, Lorentz kuvveti merkezcil kuvvete eşittir. Böylece dairenin yarıçapı hesaplanır.
Parçacığın dairesel yolunun T zaman periyodu, hızın çevresidir. R'nin değerini değiştirerek, T elde edilir.
Hız manyetik alana dik değilse, manyetik alana paralel bileşen etkilenmeden kalır ve böylece manyetik alan boyunca sabit bir hareket üretir. Bu nedenle, parçacık sarmal bir yolda hareket eder.
Yarıçap formülünde, hızın dik bileşeni ikame edilir. T hızdan bağımsız olduğu için aynı kalır.
Perdesi, hız ve periyodun paralel bileşeninin çarpımı tarafından verilen bitişik dönüşler arasındaki mesafe olarak tanımlanır.

<ol>
	<li>Stax'ı açın. (2019). Üniversite Fiziği Cilt 2. [Web versiyonu], bölüm 11.3, sayfa 501–506. <a href="https://openstax.org/books/university-physics-volume-2/pages/11-3-motion-of-a-charged-particle-in-a-magnetic-field">Yüklü Bir Parçacığın Manyetik Alandaki Hareketi'nden alındı</a></li>.
</ol>

manyetik alanda yüklü parçacığın hareketi

Bir yüklü parçacık, bir manyetik alanda hareket ettiğinde bir kuvvet deneyimler. Manyetik alanın homojen olduğunu ve yüklü parçacığın ona dik bir şekilde hareket ettiğini varsayalım. Eğer alanda bir vakum varsa, manyetik alan hareketi belirleyen baskın faktördür. Manyetik kuvvet, hareket yönüne dik olduğu için, yüklü bir parçacık eğri bir yol izler. Parçacık, tam bir daire oluşturana kadar bu eğri yolu izlemeye devam eder. Bunun başka bir şekilde ifade edilmesi ise manyetik kuvvetin her zaman hızın dik olduğu bir yöne dik olduğudur, bu yüzden yüklü parçacık üzerinde iş yapmaz. Parçacığın kinetik enerjisi ve hızı dolayısıyla sabit kalır. Kuvvet, hareketin yönünü etkiler ancak hızı etkilemez. Bundan dolayı, parçacık bir dairede hareket eder. Yüklü parçacığın daire yolunu dolaşması için geçen süre, periyot olarak tanımlanır, bu da bir tam döngü yapmak için seyahat edilen mesafe veya dairenin çevresi hızla bölündüğünde elde edilir.

Eğer hız manyetik alana dik değilse, hızın her bir bileşeni ayrı ayrı manyetik alanla karşılaştırılmalıdır. Manyetik alana dik olan hız bileşeni, bu hıza ve alana dik bir manyetik kuvvet üretir. Manyetik alana paralel olan bileşen, manyetik alanla aynı yönde sürekli hareket yaratır. Paralel hareket, helisin (bükülme ve yayılma) eğimini belirler ve bunun tanımı, bitişik dönüşler arasındaki mesafedir ve paralel hız bileşenine periyot ile çarpılır. Sonuç, birhelikal harekettir.

Yüklü parçacık helisel bir yol boyunca seyahat ederken, manyetik alanın homojen olmadığı bir bölgeye girebilir. Özellikle, bir parçacığın güçlü bir manyetik alandan zayıf bir alana, daha sonra tekrar güçlü bir alana seyahat ettiğini varsayalım. Parçacık, daha güçlü manyetik alan bölgesine girmeden önce geri yansıyabilir. Bu, bir dalganın çok hafif ve ince bir tel boyunca ilerleyip geriye doğru yansımasıyla benzerdir. Eğer yansıma her iki uçta da gerçekleşirse, parçacık "manyetik bir şişe"de hapsolmuş olarak adlandırılır.

Manyetik Alanda Yüklü Parçacığın Hareketi

Yüklü bir parçacık, manyetik bir alan boyunca hareket ederken bir kuvvete maruz kalır. Alanın tekdüze olduğunu ve yüklü parçacığın hareket ettiğini düşünün ...

Education

JoVE Core

Physics

Fizik

Unit 1

Ünite 1

Magnetic Forces and Fields

Manyetik Kuvvetler ve Alanlar

KEY TERMS AND CONCEPTS

TEMEL TERİMLER VE KAVRAMLAR

charged particle paths in magnetic fields

A charged particle in a magnetic field follows a path that depends on the direction of its velocity. When the field is uniform and the particle moves perpendicular to it, the magnetic field is the main factor that controls the motion, especially in a vacuum. The magnetic force is always perpendicular to the direction of motion, so the particle curves into a circle.

Because the force stays perpendicular to velocity, it does no work on the particle. The kinetic energy and speed stay constant while the direction changes. The time for one full trip around the circle is the period, and it equals the circle’s circumference divided by the speed.

If the velocity is not perpendicular to the magnetic field, the motion must be split into two parts. The perpendicular component produces the magnetic force and causes circular motion. The parallel component keeps moving in the same direction as the magnetic field, so the particle follows a helical path.

In a helix, the pitch is the distance between neighboring turns. It is equal to the parallel velocity component multiplied by the period. A charged particle can also enter a region where the magnetic field is not uniform. If it moves from a strong field into a weaker one and then back toward a stronger field, it may reflect before reaching the stronger region again.

This reflection is similar to a wave on a string bouncing from a very light, thin string toward a hard wall. If the particle reflects at both ends, it becomes trapped in a magnetic bottle.

Charged Particle Paths in Magnetic Fields

charged-particle-paths-in-magnetic-fields

magnetism

Magnetic Poles and Everyday Uses

Magnetism appears in many everyday objects, from toys and hangers to elevators, doorbells, and computer devices. Magnets have two poles, called north and south. Like poles repel each other, while unlike poles attract. Both poles can also attract unmagnetized iron. A single magnetic pole cannot be isolated, because every part of a magnet contains both a north pole and a south pole. A compass needle is a simple example of a magnet. It is a thin bar magnet suspended at its center, so it can turn...

magnetic fields

Magnetic Force on Moving Charges

Magnetic force on moving charges depends on motion, charge, and field direction. A moving charge or a current creates a magnetic field in the space around it, along with its electric field. That magnetic field can then push on other moving charges or currents in the field. A magnetic field is a vector field, so it has direction as well as strength. At any point, the field direction is the direction a compass needle’s north pole points. The field strength is defined from the force a charged...

magnetic field lines

Reading Magnetic Field Lines

Magnetic field lines show the direction and strength of a magnetic field. They make it easier to picture how a magnet acts in space. Each line forms a closed loop around the magnet. For a bar magnet, the field lines leave the north pole and curve around to the south pole. They then continue through the magnet back to the north pole. This loop has no beginning or end. Magnetic field lines follow clear rules. The magnetic field points tangent to a field line at any point. A small compass points...

magnetic flux

Magnetic Flux Through Surfaces

Magnetic flux through a surface describes how much magnetic field passes across that surface. It is measured in weber (Wb), the SI unit for magnetic flux. Magnetic flux is a scalar quantity, not a vector. Three factors shape magnetic flux. They are the magnetic field strength B, the area the field crosses, and the orientation of the field relative to the surface. For a small area element dA, the flux depends on the part of the magnetic field that is normal, or perpendicular, to that element at...

motion of a charged particle in a magnetic field

A charged particle in a magnetic field follows a path that depends on the direction of its velocity. When the field is uniform and the particle moves perpendicular to it, the magnetic field is the main factor that controls the motion, especially in a vacuum. The magnetic force is always perpendicular to the direction of motion, so the particle curves into a circle. Because the force stays perpendicular to velocity, it does no work on the particle. The kinetic energy and speed stay constant...

magnetic force

Magnetic Fields and Moving Charges

Magnetic fields and moving charges create magnetic force. A moving electric charge, or a current made of many moving charges, produces a magnetic field. When another current or moving charge enters that field, it feels a magnetic force in response. At the atomic level, magnetic forces come from interactions between moving electrons in the atoms of two bodies. The strength of magnetic force depends on several factors. It increases with the size of the charge and with the strength of the...

magnetic force on a current-carrying conductor

magnetic-force-on-a-current-carrying-conductor

Current and Magnetic Field Around a Wire

A current-carrying wire creates a magnetic field around it, and moving charges feel a force in that field. Because the magnetic field produced by moving charges is proportional to current, the wire itself acts as a source of magnetic field. A compass placed near the wire shows this effect by lining up tangentially around the wire. The magnetic field around a straight wire forms concentric circular loops. The right-hand rule helps determine the direction of those loops. If the thumb points in...

magnetic force on current-carrying wires: example

magnetic-force-on-current-carrying-wires-example

Balancing Weight with Magnetic Force

Magnetic force can balance the weight of a current-carrying wire when the wire sits in a magnetic field. Moving charges in the wire feel a force, so the wire itself can be pushed upward or downward. This example uses a flexible wire that is 40 cm long and has a mass of 10 g. It is held in a horizontal position inside a constant 0.40 T magnetic field. The goal is to find the current needed to remove the tension in the supporting leads. To do that, a free-body diagram is drawn first. The diagram...

force on a current loop in a magnetic field

force-on-a-current-loop-in-a-magnetic-field

Current Loops and Torque in Motors

Current loops in a magnetic field create the torque that drives a DC motor. A DC motor converts electrical energy into mechanical work. In a motor, wire loops sit inside a magnetic field. When current flows through the loops, the magnetic field pushes on them and makes the shaft rotate. The current is reversed when the loop lines up with the magnetic field. This keeps the torque on the loop going in the same direction. A commutator and brushes handle this reversal. The commutator switches the...

torque on a current loop in a magnetic field

torque-on-a-current-loop-in-a-magnetic-field

Current Loop Torque in Electric Motors

Current loop torque in electric motors shows how magnetic force can make a wire loop rotate. In an electric motor, loops of wire sit between magnets in a magnetic field. When current flows through the loops, the field applies torque. This rotation turns a shaft and converts electrical energy into mechanical energy. A rectangular current-carrying loop with N turns in a uniform magnetic field has zero net force. Even so, it can still experience net torque. The torque depends on the current I,...

the hall effect

Hall Voltage and Charge Carriers

Hall voltage and charge carriers are explained through Edwin H. Hall’s 1879 experiment. His setup helped identify the polarity of the main charge carriers in a conducting material. It also showed, for the first time, that the charge carriers in most metals are negative. A metal slab is placed in a constant magnetic field. The electrons move from right to left, so the magnetic force pushes them toward the top edge of the slab. This leaves excess negative charge at the top and excess positive...

thomson's e/m experiment

Electron Speed Selector in Thomson’s Tube

A velocity selector uses electric and magnetic fields to choose charged particles with one speed from a beam. Many beams from a heated cathode contain particles moving at different speeds, so this setup helps produce a uniform beam. The electric and magnetic fields are perpendicular to the particle’s motion and to each other. In this arrangement, a particle with charge q, speed v, and mass m enters from the top. The magnetic field points into the plane of the paper, and the electric field...

key terms and concepts

Explore how charged particles move in magnetic fields, from circular motion to helical paths and magnetic bottles, with clear high school physics terms.

Charged Particle Paths in Magnetic Fields | JoVE K12

physics

JoVE Temel Fizik, kinematik, dinamik, akışkanlar mekaniği, statik, dalgalar ve akustik dahil olmak üzere temel fizik konularının teorisini ve uygulamasını kısa ve anlaşılması kolay animasyonlu videolarla tanıtıyor. Ek olarak, sektör içindeki bilim insanı videoları, dünya çapındaki günümüz laboratuvarlarında gerçekleştirilen klasik ve orijinal araştırma deneylerinde ilgili kavramların uygulanmasını göstermektedir.

ohios-learning-standards-and-model-curriculum

Ohio’s Learning Standards and Model Curriculum

Electricity And Magnetism

Electromagnetic interactions

Tennessee Academic Standards

High School

Energy

PHYS.PS3.9

Virginia  Standards of Learning

HIgh School

PS.9

PS.9.d

PH.7

PH.7.a

PH.7.b

Minnesota Academic Standards in Science

3.1.1 9P.2.2.1.3

Arizona Science Standards

HS.P2

HS.P2U1.5

Alabama Course of Study Science

waves-and-their-applications-in-technologies-for-information-transfer

Waves and Their Applications in Technologies for Information Transfer

9-12.PS.2.3.b

Next Generation Science Standards

Motion and Stability: Forces and Interactions

HS-PS2-4

HS-PS2-5

Florida Department of Education

SC.912.P.10

SC.912.P.10.16

Texas Essential Knowledge and Skills

PHYS.6

PHYS.6.B

new-york-state-science-learning-standards

New York State Science Learning Standards

HS. Forces and Interactions

HS-PS2-5.

HS. Energy

HS-PS3-5.

Position and Displacement

The position of an object defines its location relative to a convenient frame of reference at any particular time. A frame of reference is an arbitrary ...

Average Velocity

To calculate the other physical quantities in kinematics, we must introduce the time variable. The time variable allows us not only to state the position ...

Instantaneous Velocity - I

The average velocity during a time interval cannot tell us how fast or in what direction a particle is moving at any given time during the interval. To ...

Instantaneous Velocity - II

Instantaneous velocity is the quantity that measures how fast an object is moving along its path. In other words, the instantaneous velocity of an object ...

Average Acceleration

The importance of understanding acceleration spans our day-to-day experiences, as well as the vast reaches of outer space and the tiny world of subatomic ...

Instantaneous Acceleration

Acceleration is in the direction of the change in velocity, but it is not always in the direction of motion. When an object slows down, its acceleration ...

Position and Displacement Vectors

To describe the motion of an object, one should first be able to describe its position (where it is at any particular time). More precisely, the position ...

average-and-instantaneous-velocity-vectors

Average and Instantaneous Velocity Vectors

To calculate other physical quantities in kinematics, the time variable must be introduced. The time variable not only allows us to state where an object ...

Acceleration Vectors

In everyday conversation, accelerating means speeding up. Acceleration is a vector in the same direction as the change in velocity, &#916;v, therefore the ...

Direction of Acceleration Vectors

Acceleration occurs when velocity changes in magnitude (an increase or decrease in speed), direction, or both. Although acceleration is in the direction ...

Linear Momentum

The term momentum is used in various ways in everyday language, most of which are consistent with the precise scientific definition. Generally, momentum ...

Force and Momentum

Force and momentum are intimately related. Force acting over time can change momentum, and Newton&#39;s second law of motion can be stated in its most ...

Analyze and interpret data to explain the motion of an object moving with a constant velocity or that is accelerating.

PS.PSc.4.1

Electrical Current

Electrical current is defined as the rate at which charge flows. When there is a large current present, such as that used to run a refrigerator, a large ...

Drift Velocity

The high speed of electrical signals results from the fact that the force between charges acts rapidly at a distance. Thus, when a free charge is forced ...

Current Density

The total amount of current flowing through one unit value of a cross-sectional area is referred to as current density. If the current flow is uniform, ...

Resistivity

When a voltage is applied to a conductor, an electrical field is generated, and charges in the conductor feel the force due to the electrical field. The ...

Resistance

When a current moves through any conductor, the conductor causes some level of difficulty for the current to flow. The measure of that difficulty is known ...

Ohm's Law

Many materials exhibit a simple relationship between the values of current, voltage, and resistance, known as Ohm&#8217;s law. The current that flows ...

Non-ohmic Devices

In most substances, the current flow is proportional to the voltage applied to it. A simple relationship between the values of current, voltage, and ...

Construct an explanation to compare simple series and parallel circuits in terms of Ohm's Law.

PS.PSc.6.2

Continuity Equation

The total amount of current flowing per unit cross-sectional area is called the current density. Hence, the current passing through a cross-sectional area ...

Boundary Conditions for Current Density

Current density becomes discontinuous across an interface of materials with different electrical conductivities. The normal component of the current ...

Electrical Conductivity

In perfect conductors, the electric field inside is always zero due to the abundance of free electrons, which nullify any field by flowing. As a result, ...

Theory of Metallic Conduction

The conduction of free electrons inside a conductor is best described by quantum mechanics. However, a classical model makes predictions close to the ...

Obtain, evaluate, and communicate information to explain how current is affected by changes in composition, length, temperature, and diameter of wire.

PS.PSc.6.3

Magnetism

Magnets are commonly found in everyday objects, such as toys, hangers, elevators, doorbells, and computer devices. Experimentation on these magnets shows ...

Magnetic Fields

A moving charge or a current creates a magnetic field in the surrounding space, in addition to its electric field. The magnetic field exerts a force on ...

Magnetic Field Lines

The representation of magnetic fields by magnetic field lines is very useful in visualizing the strength and direction of the magnetic field. Each of the ...

Magnetic Flux

The magnetic flux measures the number of magnetic field lines passing through a given surface area. The SI unit for magnetic flux is the weber (Wb). ...

A charged particle experiences a force when moving through a magnetic field. Consider the field to be uniform and the charged particle to move ...

Magnetic Force

In addition to the electric forces between electric charges, moving electric charges exert magnetic forces on each other. A magnetic field is created by a ...

Magnetic Force On A Current-Carrying Conductor

Moving charges experience a force in a magnetic field. Since the magnetic fields produced by moving charges are proportional to the current, a conductor ...

Magnetic Force On Current-Carrying Wires: Example

In a magnetic field, moving charges encounter a force. If a wire contains these moving charges, i.e., if the wire is carrying a current, then a force acts ...

Force On A Current Loop In A Magnetic Field

Magnetic forces on wires carrying current are most frequently applied in motors. A DC motor is a device that converts electrical energy into mechanical ...

Torque On A Current Loop In A Magnetic Field

The most common application of magnetic force on current-carrying wires is in electric motors. These consist of loops of wire, which are placed between ...

The Hall Effect

Edwin H. Hall, in the year 1879, devised an experiment that could be used to identify the polarity of the predominant charge carriers in a conducting ...

Magnetic Field due to Moving Charges

A stationary charge creates and interacts with the electric field, while a moving charge creates a magnetic field.
Consider a point charge moving with a ...

Biot-Savart Law

The Biot-Savart law gives the magnitude and direction of the magnetic field produced by a current. This empirical law was named in honor of two ...

Biot-Savart Law: Problem-Solving

The magnitude and direction of a magnetic field created by a steady current can be calculated using the Biot-Savart law.
Consider a mobile phone battery ...

Magnetic Field Due to Two Straight Wires

Consider two parallel straight wires carrying a current of 10 A and 20 A in the same direction and separated by a distance of 20 cm. Calculate the ...

magnetic-force-between-two-parallel-currents

Magnetic Force Between Two Parallel Currents

Two long, straight, and parallel current-carrying conductors exert a force of equal magnitude on one another. The direction of the force depends on the ...

Magnetic Field Of A Current Loop

Consider a circular loop with a radius a, that carries a current I. The magnetic field due to the current at an arbitrary point P along the axis of the ...

Use models to explain magnetism in terms of domains, interactions of poles, and magnetic fields.

Analyze motion in terms of speed, velocity, acceleration, and momentum.

Charged Particle Paths in Magnetic Fields

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