Name: balancing weight with magnetic force
Uploaded: 2025-05-22T09:05:51.000Z
Duration: 1 min 22 s
Channel: JoVE

K12 Standards

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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

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

Magnetic Force On Current-Carrying Wires: Example

Рассмотрим проводник в плоскости XY, несущий ток влево. Проводник состоит из двух прямых отрезков длиной L, параллельных оси x, и полуокружности радиусом R.
Если проводник помещен в равномерное магнитное поле перпендикулярно плоскости провода, направленное наружу, определяют общую магнитную силу на проводнике.
Во-первых, определите магнитную силу для отдельных прямых участков, несущих ток в направлении x.
Во-вторых, разделим искривленный отрезок на бесконечно малые прямые участки, имеющие длину dl под углом тета.
Бесконечно малая длина и магнитное поле перпендикулярны друг другу, а направление их перекрестного произведения радиально наружу. Таким образом, можно определить величину и составляющие силы на сечениях.
Интегрируя выражение относительно тета, можно определить силу, действующую на весь изогнутый проводник.
Наконец, сложив силы на всех трех секциях, можно получить общую силу на проводнике в положительном направлении y.

<ol>
	<li>OpenStax. (2019). Университетская физика Том 2. [Веб-версия], стр. 396 - 398. Получено из <a href="https://openstax.org/books/university-physics-volume-2@8ede2ba/pages/11-4-magnetic-force-on-a-current-carrying-conductor">https://openstax.org/books/university-physics-volume-2@8ede2ba/pages/11-4-magnetic-force-on-a-current-carrying-conductor</a></li>
</ol>

Магнитная сила на проводах, по которым течёт ток: Пример

В магнитном поле движущиеся заряды испытывают силу. Если провод содержит эти движущиеся заряды, то на провод также действует сила. Рассмотрим пару гибких отводов, удерживающих провод длиной 40 см и весом 10 г в горизонтальном положении. Провод помещается в постоянное магнитное поле с индукцией 0,40 Т, как показано на рисунке 1 (a). Определите величину и направление тока в проводе, необходимые для снятия натяжения в поддерживающих отводах.

Для решения этой задачи нарисуйте силовую схему системы, как показано на рисунке 1 (b). Затем, используя правило правой руки, определите направление магнитной силы, действующей на провод. И, наконец, приравняйте две силы, чтобы определить ток в проводе.

<img alt="Equation1" src="/files/ftp_upload/13769/13769_Figure_1.png" style="text-align: center;" />

В силовой схеме натяжение в поддерживающих отводах равно нулю, когда силы магнитного и гравитационного воздействия сбалансированы. Используя правило правой руки, магнитная сила направлена вверх, и приравнивая две силы - силу веса и магнитную силу на проводе:

<img alt="Equation2" src="/files/ftp_upload/13769/13769_Equation_2.svg" style="text-align: center; height: 20px;" />

<img alt="Equation3" src="/files/ftp_upload/13769/13769_Equation_3.svg" style="text-align: center; height: 50px;" />

Ток в проводе может быть определён. Большое магнитное поле создаёт значительную силу на участке провода, чтобы противостоять весу провода.

В магнитном поле движущиеся заряды наталкиваются на силу. Если провод содержит эти движущиеся заряды, т.е. если провод несет ток, то действует сила...

Education

JoVE Core

Physics

Физика

Unit 1

Раздел 1

Magnetic Forces and Fields

Магнитные силы и поля

KEY TERMS AND CONCEPTS

ОСНОВНЫЕ ТЕРМИНЫ И ПОНЯТИЯ

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 shows the forces acting on the wire. Then the right-hand rule is used to find the direction of the magnetic force on the wire.

When the tension in the leads is zero, the magnetic force and the gravitational force are balanced. The magnetic force points up, so it can counter the wire’s weight. By setting the weight equal to the magnetic force, the current in the wire can be determined. The strong magnetic field produces a large enough force on the wire to support its weight.

Balancing Weight with Magnetic Force

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

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

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...

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 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

Find out how a current-carrying wire can be supported by a magnetic field. Use a free-body diagram and the right-hand rule to solve for current.

Balancing Weight with Magnetic Force | 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.

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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

Alabama Course of Study Science

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Waves and Their Applications in Technologies for Information Transfer

9-12.PS.2.3.b

Florida Department of Education

SC.912.P.10

SC.912.P.10.10

Position and Displacement

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Instantaneous Velocity - II

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Average and Instantaneous Velocity Vectors

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

PS.PSc.4.1

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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 ...

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Resistance

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

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PS.PSc.6.3

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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). ...

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Magnetic Force

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Magnetic Force On A Current-Carrying Conductor

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magnetic-force-between-two-parallel-currents

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A fundamental property of a static magnetic field is that it is not conservative, unlike an electrostatic field. Instead, there is a relationship between ...

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Induction

An emf is induced when the magnetic field in a coil is changed by pushing a bar magnet into or out of the coil. emfs of opposite signs are produced by ...

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Lenz's Law

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PS.PSc.6.5

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

Balancing Weight with Magnetic Force

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