Name: induced current from changing magnetic flux
Uploaded: 2023-04-30T12:42:51.000Z
Duration: 1 min 22 s
Channel: JoVE

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Motion and Stability- Forces and Interactions

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Motional Emf

Рассмотрим проводящий стержень длины L, движущийся с постоянной скоростью v в магнитном поле B, направленном в плоскость экрана.
Магнитная сила, действующая на положительный заряд внутри проводящего стержня, направлена вверх, в результате чего противоположные заряды накапливаются на обоих концах стержня. При этом создается электрическое поле, направленное вниз.
Заряды продолжают накапливаться до тех пор, пока электрическая сила не станет достаточно большой, чтобы уравновесить магнитную силу. Разность потенциалов на стержне присутствует до тех пор, пока он движется.
Если этот стержень образует замкнутый проводящий контур со стационарным U-образным проводником, то свободные заряды от стержня перераспределяются по контуру. Он генерирует ток в замкнутом контуре, а движущийся стержень генерирует движущую электродвижущую силу, известную как движущаяся ЭДС.
В этом случае магнитный поток, проходящий через замкнутый контур, равен магнитному полю, умноженному на площадь петли. Согласно закону Фарадея, скорость изменения магнитного потока равна величине движущейся ЭДС.

<ol>
	<li>Янг, Х.Д. и Фридман, Р.А. (2012). Университетская физика с современной физикой. Сан-Франциско, Калифорния: Пирсон. Раздел 29.4, страницы 969-970.</li>
	<li>OpenStax. (2019). Университетская физика Том 2. [Веб-версия]. Раздел 13.1, страницы 591-592. Получено из <a href="https://openstax.org/books/university-physics-volume-2/pages/13-3-motional-emf">https://openstax.org/books/university-physics-volume-2/pages/13-3-motional-emf</a></li>
</ol>

Мотивирующая ЭДС

Магнитный поток зависит от трёх факторов: силы магнитного поля, площади, через которую проходят линии поля, и ориентации поля относительно поверхности. Если одно из этих значений меняется, происходит соответствующее изменение магнитного потока. Если меняется площадь, через которую проходят линии магнитного поля, меняется и магнитный поток. Это изменение площади может быть двух типов: поток через прямоугольную петлю увеличивается при движении в магнитное поле или изменяется магнитный поток через вращающуюся катушку.

Если проводящая стержень движется через магнитное поле перпендикулярно движению стержня, то в стержне возникает (ЭДС). Эта индуцированная (ЭДС) создаёт индуцированный ток, когда проводящий стержень образует замкнутую проводящую петлю с U-образным проводником. Величина и направление индуцированной (ЭДС) могут быть определены с использованием закона Фарадея и закона Ленца. В таких системах закон сохранения энергии требует, чтобы мощность, поставляемая из-за движения стержня, и мощность, рассеиваемая из-за индуцированного тока, были равными.

Этот принцип можно увидеть в работе электромагнитной пушки. В электромагнитной пушке проводящий стержень заменяется снарядом или оружием, которое должно быть выпущено. В этом типе пушки оптимальное отключение/постепенное снижение магнитного поля уменьшает поток между рельсами, вызывая ток, который толкает снаряд. Этот ток через якорь обладает магнитной силой и направляет снаряд вперед. Однако электромагнитные пушки не широко применяются в военных целях из-за высокой стоимости производства и высоких токов.

Магнитный поток зависит от трех факторов: силы магнитного поля, площади, через которую проходят силовые линии, и ориентации поля.

Education

JoVE Core

Physics

Физика

Unit 1

Раздел 1

Electromagnetic Induction

Электромагнитная индукция

KEY TERMS AND CONCEPTS

ОСНОВНЫЕ ТЕРМИНЫ И ПОНЯТИЯ

induced current from changing magnetic flux

Induced current from changing magnetic flux depends on how a magnetic field interacts with an area. Magnetic flux changes when the field strength changes, when the area it passes through changes, or when the field turns relative to the surface. When any of these factors vary, the magnetic flux also varies.

A change in area can happen in two common ways. The flux through a rectangular loop increases as the loop moves into a magnetic field. The magnetic flux through a rotating coil also changes as the coil turns. These changes can create an emf, or electromotive force, in a conductor.

If a conducting rod moves through a magnetic field and its motion is perpendicular to the rod, an emf is induced in the rod. That induced emf can produce an induced current when the rod is part of a closed loop with a U-shaped conductor. Faraday's law and Lenz's law are used to determine the size and direction of the induced emf.

These systems also show conservation of energy. The power from the rod's motion equals the power lost as heat from the induced current. The same idea appears in a rail gun, where the conducting rod is replaced by a projectile or weapon. When the magnetic field is shut off or ramped down, the flux between the rails decreases, current flows in the rod holding the projectile, and the armature feels a magnetic force that pushes it forward. Rail guns are not widely used in the military because they are expensive to build and require very high currents.

Induced Current from Changing Magnetic Flux

induced-current-from-changing-magnetic-flux

induction

Magnetic Flux and Induced Current

Magnetic flux and induced current are linked when a magnetic field changes near a coil. Moving a bar magnet into or out of a coil induces an emf, which is an electromotive force. If the motion goes in the opposite direction, the emf has the opposite sign. Reversing the magnet poles also reverses the direction of the induced emf. The same effect appears when the coil moves instead of the magnet. Relative motion is what matters. A faster motion produces a larger emf. If the magnet and coil stay...

ampere-maxwell's law: problem-solving

Displacement Current in an RC Circuit

Displacement current in an RC circuit can be found by tracking the charging capacitor. A parallel-plate capacitor with capacitance C, plate area A, and plate separation d is connected to a resistor R and a battery of voltage V. When the current starts to flow at t = 0, the charge and voltage on the capacitor change with time. The first step is to use the RC-circuit result for the capacitor voltage at time t. With the z-axis pointing from the positive plate to the negative plate, the electric...

differential form of maxwell's equations

Maxwell’s Equations at a Point

Maxwell’s equations at a point describe how electric and magnetic fields change in space and time. They connect field behavior to charge and current density at a single location. This point-by-point form is useful when studying electromagnetic fields in detail. James Clerk Maxwell was a major physicist of the nineteenth century. He combined earlier laws of electricity and magnetism into one electromagnetic theory. The basic experimental laws came from scientists such as Oersted, Coulomb,...

dc generator

How a DC Generator Makes Current

A DC generator makes electrical energy from mechanical motion. It produces DC pulses with the same polarity, unlike an alternator, which gives sinusoidal AC current. The two machines have similar construction, but a DC generator uses a single split ring instead of a pair of slip rings. That split ring is called a commutator. It works like a rotary switch that changes the contact with the brushes after each half turn of the conducting loop. This action keeps the induced emf at the same...

magnetic damping

Eddy Currents and Magnetic Braking

Eddy currents can create strong drag on moving objects. This drag is called magnetic damping. A metallic pendulum bob swinging between the poles of a strong magnet feels this force as it enters and leaves the field, so its motion dies out quickly. The effect is much smaller for a slotted metal plate. As the plate enters the magnetic field, a changing flux induces an emf, or electromotive force. The slots limit the size of the current loops, and nearby loops can carry currents in opposite...

superconductor

Superconductor Critical Temperature

Superconductivity is the state in which a material has no electrical resistance and magnetic fields cannot penetrate it. A material that reaches this state is called a superconductor. The key idea in the transcript is the critical temperature, which is the temperature at which the change happens. Heike Kamerlingh Onnes of Leiden University first observed this behavior in mercury in 1911. He cooled a mercury sample in liquid helium to study how resistance changed with temperature. As the...

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Superconductors and Magnetic Levitation

Superconductors are materials that can carry electric current with zero resistance when they are cooled below a critical temperature. At this point, they also show the Meissner effect, which means they push magnetic fields out of their interior. A light permanent magnet can then levitate in a stable position above the superconducting sample. This magnetic levitation has real uses. High-speed trains have been built with strong superconducting magnets so they can float above the track and avoid...

faraday's law

Magnetic Flux and Induced Emf

Faraday’s law connects magnetic flux changes to induced emf, or voltage. A change in the magnetic field or in the coil’s orientation with respect to the field can produce this voltage. Magnetic flux describes how many magnetic field lines pass through a given surface area.

lenz's law

Magnet Motion and Induced Current

Magnet motion and induced current are linked by Lenz’s law. The law says that the induced emf, or electromotive force, drives current around a wire loop in a direction that opposes the change in magnetic flux that caused it. A moving bar magnet can create this effect in a coil. If the magnet moves toward the coil, the magnetic flux increases and an induced current appears. That current produces a magnetic field that pushes against the stronger field from the magnet. The same idea works in...

motional emf

Induced current from changing magnetic flux depends on how a magnetic field interacts with an area. Magnetic flux changes when the field strength changes, when the area it passes through changes, or when the field turns relative to the surface. When any of these factors vary, the magnetic flux also varies. A change in area can happen in two common ways. The flux through a rectangular loop increases as the loop moves into a magnetic field. The magnetic flux through a rotating coil also changes...

faraday disk dynamo

Faraday Disk Dynamo and DC Output

A Faraday disk dynamo is a DC generator that produces an emf constant in time. It uses a conducting disk that spins at constant angular velocity in a magnetic field. The magnetic field is perpendicular to the plane of the disk. As the disk rotates, the magnetic flux changes and an emf is induced. This causes opposite charges to build up at the rim and at the center of the disk. The direction of the induced emf depends on the direction of the magnetic field and the direction of rotation. If...

induced electric fields

Faraday’s Law and Induced EMF

Faraday’s law explains how a changing magnetic flux can create an induced emf in a circuit. When current is induced, work is being done on the conduction electrons in the wire. That work must come from a source, and the source is not a battery or a magnetic field. A battery does not have to be present in a circuit for current to be induced. Magnetic fields also do not do work on moving charges. Instead, the change in magnetic flux produces an electric field in the wire. This is called an...

induced electric fields: applications

Electric Fields from Changing Magnetism

An electric field can be induced by a changing magnetic field. This induced electric field is nonconservative, which means it does not do net work when a charge moves around a closed path. That behavior is different from an electrostatic field, which comes from a fixed charge distribution. An electrostatic field is conservative, so it does no net work over a closed path. Because of this difference, electric potential can be linked to the electrostatic field, but not to the induced field. When...

eddy currents

Eddy Currents in Recycling, Brakes, and Heat

Eddy currents affect how metals move, stop, and heat up. They form only in conductors, so they are useful for separating metals from nonmetals and for other practical devices. In recycling centers, trash can be sent down a ramp under a strong magnet. Metals in the trash slow down because eddy currents resist their motion. Nonmetals keep moving, so the materials separate. This method works for metals in general, not only ferromagnetic ones. Eddy currents also help in metal detectors. A...

displacement current

Maxwell’s Fix for Changing Currents

Maxwell’s correction to Ampère’s law explains how changing electric fields can create magnetic fields. The key idea is the displacement current, Id, which Maxwell added to the real conduction current, I. This extra term helps the law work when current is not steady. The displacement current is defined using the permittivity of free space, ε0, and the electric flux, ΦE. It is not a real flow of charge. Instead, it is an added term in Maxwell’s equations that acts like current in Ampère’s law. <br...

significance of displacement current

Maxwell’s Fix for Charging Capacitors

Maxwell’s fix for a charging capacitor is the displacement current in Ampère’s law. A displacement current is not a flow of charge like conduction current. It comes from a changing electric field. That is why it is defined using a time-varying electric field and has its own displacement current density. Maxwell added this term to the original Ampère’s law. The result is called generalized Ampère’s law. The added displacement current term lets the law work in regions where no charges are moving.

electromagnetic fields

Electric and Magnetic Fields in Motion

Electric and magnetic fields can come from different sources, but they can act in surprisingly similar ways. Static charges create electrostatic fields. These fields are conservative, which means a test charge does no net work after moving around a complete loop. Fields made by changing magnetic fields behave differently. They are not conservative, and they do net work on a charge. That work is proportional to how fast the magnetic flux changes. These fields also do not follow Gauss’s law for...

maxwell's equation of electromagnetism

Maxwell's Equations and Light Waves

Maxwell's equations bring electricity, magnetism, and light together in one electromagnetic theory. James Clerk Maxwell was a major nineteenth-century physicist, and his work helped shape modern physics. He also made important contributions to the kinetic theory of gases, color vision, and the study of Saturn's rings. Maxwell built on earlier experiments in electricity and magnetism from Oersted, Coulomb, Gauss, and Faraday. These physicists had discovered the basic laws separately. Maxwell...

symmetry in maxwell's equations

Electric and Magnetic Field Symmetry

Electric and magnetic field symmetry is a key part of Maxwell's equations. After the fields are calculated with Maxwell's four equations, the Lorentz force equation gives the force those fields exert on a charged particle moving at a certain velocity. The Lorentz force law combines the effect of the electric field and the magnetic field on the moving charge. Maxwell's equations and the Lorentz force law together describe electricity and magnetism. The symmetry in Maxwell's framework is easier...

electric generator: alternator

How Alternators Produce AC Power

Alternators produce alternating current by rotating a conducting loop in a magnetic field. As the loop turns inside the field, the magnetic flux through the coil changes with time. That changing flux induces an emf, or electric voltage, in the circuit. A simple alternator uses a loop placed in a uniform magnetic field. The loop connects to split rings, and brushes carry the current to the external circuit. As the loop rotates, the magnetic flux changes sinusoidally, so the induced emf also...

back emf

Motor Current and Speed Changes

Motor current and speed changes are linked by back emf in an electric motor. A motor sends current through a wire loop in a magnetic field. The magnetic field pushes on the loop and creates torque, which turns a shaft and does mechanical work. As the coil turns, the magnetic flux through it changes. That changing flux induces an emf, or voltage, by Faraday’s law. The motor then acts like a generator whenever its coil rotates, whether the shaft is turned by an external drive or by the motor...

key terms and concepts

Explore how changing magnetic flux creates induced emf and current in loops, rods, and rail guns, using Faraday's law, Lenz's law, and energy conservation.

Induced Current from Changing Magnetic Flux | JoVE K12

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Induced Current from Changing Magnetic Flux

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