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

전하 Q의 점 질량 m이 균일한 자기장 B에 수직으로 움직인다고 가정합니다.
로렌츠 힘의 크기는 일정하며 항상 속도에 수직입니다. 따라서 속도의 크기는 변경할 수 없으며 방향만 변경할 수 있습니다. 따라서 입자의 경로는 반지름이 r인 원입니다.
뉴턴의 운동 제2법칙을 사용하면 로렌츠 힘은 구심력과 같습니다. 따라서 원의 반지름이 계산됩니다.
입자의 원형 경로의 시간 주기 T는 속도에 의한 원주입니다. r의 값을 대체하면 T가 얻어집니다.
속도가 자기장에 수직이 아닌 경우 자기장에 평행한 구성 요소는 영향을 받지 않고 유지되므로 자기장을 따라 일정한 움직임을 생성합니다. 따라서 입자는 나선형 경로로 이동합니다.
반지름에 대한 공식에서는 속도의 수직 구성 요소가 대체됩니다. T는 속도와 무관하기 때문에 동일하게 유지됩니다.
그 피치는 속도와 주기의 평행 구성 요소의 곱에 의해 주어지는 인접한 회전 사이의 거리로 정의됩니다.

<ol>
	<li>오픈스택스. (2019). 대학 물리학 Vol. 2. [웹 버전], 섹션 11.3, 501–506페이지. 원본 주소 <a href="https://openstax.org/books/university-physics-volume-2/pages/11-3-motion-of-a-charged-particle-in-a-magnetic-field">Motion of a Charged particle in a Magnetic Field</a></li>
</ol>

자기장 내 하전 입자의 움직임

하전입자는 자기장을 통과할 때 힘을 받습니다. 필드가 균일하고 하전 입자가 필드에 수직으로 움직이는 것을 고려하십시오. 자기장이 진공 상태에 있으면 자기장이 운동을 결정하는 주요 요인이 됩니다. 자기력은 운동 방향에 수직이므로 대전 입자는 곡선 경로를 따릅니다. 입자는 완전한 원을 형성할 때까지 이 곡선 경로를 계속 따라갑니다. 이를 보는 또 다른 방법은 자기력이 항상 속도에 수직이므로 하전 입자에 작용하지 않는다는 것입니다. 따라서 입자의 운동 에너지와 속도는 일정하게 유지됩니다. 힘은 운동 방향에 영향을 주지만 속도에는 영향을 미치지 않습니다. 따라서 입자는 원을 그리며 움직입니다. 하전 입자가 원형 경로를 따라 이동하는 데 걸리는 시간은 주기로 정의되며, 이는 하나의 완전한 주기를 만들기 위해 이동한 거리 또는 원의 원주를 속도로 나눈 것과 같습니다.

속도가 자기장과 수직이 아닌 경우 속도의 각 구성 요소를 자기장과 별도로 비교해야 합니다. 자기장에 수직인 속도 성분은 이 속도와 자기장 모두에 수직인 자기력을 생성합니다. 자기장과 평행한 구성요소는 자기장과 동일한 방향을 따라 일정한 운동을 생성합니다. 평행 운동은 인접한 회전 사이의 거리로 정의되는 나선의 피치를 결정합니다. 이는 속도의 평행 성분과 주기를 곱한 것과 같습니다. 결과는 나선형 운동입니다.

하전입자는 나선형 경로를 따라 이동하는 동안 자기장이 균일하지 않은 영역에 들어갈 수 있습니다. 특히, 입자가 강한 자기장의 영역에서 약한 자기장의 영역으로 이동한 다음 다시 강한 자기장의 영역으로 돌아간다고 가정합니다. 입자는 더 강한 자기장 영역에 들어가기 전에 다시 반사될 수 있습니다. 이는 매우 가볍고 얇은 끈에서 단단한 벽으로 이동하여 뒤로 반사되는 끈의 파동과 유사합니다. 반사가 양쪽 끝에서 발생하면 입자는 소위 자성병에 갇히게 됩니다.

하전 입자는 자기장을 통해 이동할 때 힘을 받습니다. 필드가 균일하고 하전 입자가 이동하는 것을 고려하십시오 ...

Education

교육

JoVE Core

Physics

물리학

Unit 1

제1단원

Magnetic Forces and Fields

자기력과 자기장

KEY TERMS AND CONCEPTS

주요 용어 및 개념

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 Core Physics introduces the theory and application of fundamental physics topics, including kinematics, dynamics, fluid mechanics, statics, waves, and acoustics, with concise and easy-to-understand animated videos. Additionally, the scientist-in-action videos demonstrate the application of related concepts in classical and original research experiments performed in today's laboratories worldwide.

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

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Average Velocity

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Instantaneous Velocity - I

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average-and-instantaneous-velocity-vectors

Average and Instantaneous Velocity Vectors

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Acceleration Vectors

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PS.PSc.4.1

Electrical Current

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Drift Velocity

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Current Density

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Resistivity

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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

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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

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Theory of Metallic Conduction

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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

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Magnetic Force On Current-Carrying Wires: Example

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Force On A Current Loop In A Magnetic Field

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Torque On A Current Loop In A Magnetic Field

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The Hall Effect

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Magnetic Field due to Moving Charges

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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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