Name: electric and magnetic fields in motion
Uploaded: 2026-07-09T14:53:11.681Z
Duration: 1 min 31 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.6.5

Electromagnetic Fields

Recall Gauss&#x27;s law for electric fields produced by charges and Faraday&#x27;s law for electric fields created by the time-varying magnetic flux.
Since the former follows Gauss&#x27;s law, its integral over a closed loop is zero; it is a conservative field. However, using Faraday&#x27;s law, the latter is a non-conservative field.
Moreover, since it always forms a closed loop, its flux through any closed surface is zero. Thus, it disobeys Gauss&#x27;s law.
Moving charges or steady currents produce magnetic fields which obey Amp&#xE8;re&#x27;s law. However, time-varying electric flux gives rise to magnetic fields that do not obey Amp&#xE8;re&#x27;s law.
Recall the aim of studying electromagnetism: calculate the force on a test charge so that, via Newton&#x27;s second law of motion, its trajectory can be determined.
Experiments reveal that the conservative and non-conservative electric fields, and the Amp&#xE8;re&#x27;s law obeying and disobeying magnetic fields, give rise to the same kind of Lorentz force on a test charge. Moreover, they are found to add vectorially.
Hence, they are added together and simply called electric and magnetic fields.

electromagnetic fields

Electric fields generated by static charges, often referred to as electrostatic fields, are characteristically different from electric fields created by time-varying magnetic fields. While the former is a conservative field, implying that no net work is done on a test charge if it goes around in a complete loop in the field, the latter is, by definition, not a conservative field; net work is done, and it is proportional to the rate of change of magnetic flux.
However, the observation of Gauss&#x27;s law for electrostatic fields breaks down for fields generated by changing magnetic fields, because these always form closed loops. Thus, there is no net flux through a closed surface, as the number of field lines entering and leaving is the same.
Despite their differences, experiments reveal that they exert the same kind of force, the Lorentz force, on test charges. Moreover, these forces follow the principle of superposition. Consequently, the fields also follow the principle of superposition. Hence, they are vectorially added and simply called electric fields.
The distinction between conservative (electrostatic) and non-conservative electric fields is important only in specific cases, for example, inside an ideal inductor.
Nature fascinates us through its simplicity because it was not necessary for the fields produced by different mechanisms to exert the same kind of Lorentz force and add up vectorially. The same simplicity also applies to magnetic fields.
Steady currents produce magnetic fields that obey Amp&#xE8;re&#x27;s law. However, changing electric fields also produce magnetic fields, in that the field exerts the same Lorentz force on a moving test charge and adds up vectorially with the field produced by steady currents. This observation justifies calling them both magnetic fields.

Electric fields generated by static charges, often referred to as electrostatic fields, are characteristically different from electric fields created by ...

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Education

JoVE Core

Physics

Unit 1

Electromagnetic Induction

KEY TERMS AND CONCEPTS

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 electrostatic fields, because they form closed loops. The number of field lines entering and leaving a closed surface is the same, so the net flux is zero.

Even with these differences, experiments show that both kinds of electric fields push on a test charge with the same Lorentz force. They also obey superposition, which means the fields add as vectors. For that reason, they are both called electric fields, even though their sources are different. The difference matters mainly in special cases, such as inside an ideal inductor.

The same idea applies to magnetic fields. Steady currents produce magnetic fields that follow Ampère’s law. Changing electric fields also produce magnetic fields. These fields exert the same Lorentz force on a moving test charge and add vectorially with the fields from steady currents. That is why they are all treated as magnetic fields.

Electric and Magnetic Fields in Motion

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...

types of superconductors

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

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.

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 static charges, changing magnetic fields, and steady currents create electric and magnetic fields that add by superposition and act through the Lorentz force.

Electric and Magnetic Fields in Motion | 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.

PS.Phy.5.2

Pennsylvania State Academic Standards

Forces and Interactions

3.2.9-12.L

3.2.9-12.M

Louisiana Student Standards for Science

High School

Motion And Stability: Forces And Interactions

HS-PS2-5

HS-PS2-4

ohios-learning-standards-and-model-curriculum

Ohio’s Learning Standards and Model Curriculum

Electricity And Magnetism

Electromagnetic interactions

Virginia  Standards of Learning

HIgh School

PS.9

PS.9.e

new-jersey-student-learning-standards-for-science

New Jersey Student Learning Standards for Science

Motion and Stability: Forces and Interactions

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

9-12.PS.2.3.e

Next Generation Science Standards

Energy

HS-PS3-5

HS-PS4-3

Florida Department of Education

SC.912.P.10

SC.912.P.10.17

south-carolina-college-and-career-ready-science-standards

South Carolina College and Career Ready Science Standards

P-PS2-5

P-PS3-5

new-york-state-science-learning-standards

New York State Science Learning Standards

HS. Forces and Interactions

HS-PS2-5.

HS. Waves and Electromagnetic Radiation

HS-PS4-4.

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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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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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PS.PSc.6.3

Magnetism

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Magnetic Fields

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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

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

Motion Of A Charged Particle In A Magnetic Field

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Magnetic Force On A Current-Carrying Conductor

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

PS.PSc.6.4

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Electric and Magnetic Fields in Motion

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