Name: magnetic fields from charges in motion
Uploaded: 2026-07-09T14:44:22.128Z
Duration: 1 min 25 s
Channel: JoVE

K12 Standards

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

NC 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 Field due to Moving Charges

The presence of a charge produces an electric field. If the charge moves, it also creates a magnetic field.
If the positive charge moves with a constant velocity, the electric field and the magnetic field at any point are directly proportional to the charge magnitude and inversely proportional to the square of the distance between the source and the field point.
However, unlike the electric field, the direction of the magnetic field is perpendicular to the plane containing the unit vector along the line joining the point P, and the charge velocity.
For the moving charge, the magnetic field at point P is also proportional to the cross product of its velocity and the unit vector.
Adding the proportionality constant as the permeability of free space, the final expression for the magnetic field is obtained.
The expression states that the field is maximum in the plane perpendicular to the charge velocity.
Conventionally, if the thumb gives the velocity direction, then the curled fingers show the magnetic field direction. For a negative charge, the field direction reverses.

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 constant velocity. Like the electric field, the magnetic field at any point is directly proportional to the magnitude of the charge and inversely proportional to the square of the distance between the source point and the field point. However, unlike the electric field, the magnetic field is always perpendicular to the plane containing the line joining the source to the field point. The magnitude of the magnetic field is proportional to the particle&#x2019;s speed, and it also depends on the sine of the angle; the velocity vector subtends with the line joining the source and the field point (Equation1).
<img alt="Equation1" src="/files/ftp_upload/14089/14089_Equation_1.svg" style="text-align: center; height: 28px;" />
Considering a unit vector along a distance r to a field point, the equation for the magnetic field at field point P can be expressed as the cross-product of the velocity vector and the unit vector, as shown in Equation 2.&#xA0;
<img alt="Equation2" src="/files/ftp_upload/14089/14089_Equation_2.svg" style="text-align: center; height: 31px;" />
The constant, &#xB5;o, is the permeability of free space, and its value is 4&#x3C0; x 10&#x2212;7 T&#xB7;m&#xB7;A&#x2212;1.
The unit of the magnetic field is the Tesla, named after Nikola Tesla, and is expressed as &#x201C;T&#x201D;.

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 ...

https://cloudfront.jove.com/files/media/science-education/science-education-thumbs/14089.jpg

Education

JoVE Core

Physics

Unit 1

Sources of Magnetic Fields

KEY TERMS AND CONCEPTS

magnetic fields from charges in motion

A moving charge creates a magnetic field. For a point charge moving at constant velocity, the field at any point depends on the charge and the distance from the source point to the field point. It is directly proportional to the charge magnitude and inversely proportional to the square of that distance.

The magnetic field also has a direction. Unlike the electric field, it is always perpendicular to the plane formed by the line from the source to the field point. Its strength depends on the particle’s speed and on the sine of the angle between the velocity vector and that line.

The field at point P can be written as a cross product of the velocity vector and a unit vector along the distance r. This vector form shows why the magnetic field direction is tied to both motion and geometry. The constant μ0 is the permeability of free space, and its value is 4π × 10−7 T·m·A−1. The unit of magnetic field is the tesla, written as T, and it is named after Nikola Tesla.

Magnetic Fields from Charges in Motion

biot-savart law

Magnetic Field from a Current Element

The Biot-Savart law links a current-carrying wire to the magnetic field it creates. It gives both the magnitude and the direction of that field. The law is named for Jean-Baptiste Biot and Félix Savart, who studied how a straight wire carrying current interacts with a permanent magnet. A current-carrying wire produces a magnetic field around it. To describe the field from a tiny section of wire, we use an infinitesimal current element, dl. The direction of dl follows the direction of the...

biot-savart law: problem-solving

Calculating Magnetic Fields with Biot-Savart

The Biot-Savart law is used to calculate the magnetic field made by a steady current. A mobile phone battery bank and the wire between the two can be used as an example of that current. At a field point P, the goal is to find the magnitude of the magnetic field created by the current in the wire. The first step is to look at a small current element of length dl. This element is at a distance r from the field point. The known values are the current, the length of the current element, the...

A moving charge creates a magnetic field. For a point charge moving at constant velocity, the field at any point depends on the charge and the distance from the source point to the field point. It is directly proportional to the charge magnitude and inversely proportional to the square of that distance. The magnetic field also has a direction. Unlike the electric field, it is always perpendicular to the plane formed by the line from the source to the field point. Its strength depends on the...

magnetic field due to two straight wires

Net Magnetic Field at the Midpoint of Two Wires

Two parallel straight wires can create a net magnetic field at the point halfway between them. In this example, the wires carry currents of 10 A and 20 A and are separated by 20 cm. The midpoint, labeled P2, is 10 cm from each wire. The magnetic field lines around each wire form counterclockwise concentric circles. At the midpoint, the field from one wire can point in the opposite direction from the field from the other wire. The net magnetic field is found by magnetic field superposition,...

magnetic force between two parallel currents

magnetic-force-between-two-parallel-currents

Parallel Currents and the Pinch Effect

Parallel current-carrying wires can pull on each other with a magnetic force. The force has the same size on both conductors. Its direction depends on whether the currents flow in the same direction or in opposite directions. The magnetic field from one long, straight wire acts on a finite length of the other wire. The force on that wire comes from the product of its current and the cross product of its length vector with the field. Using the right-hand rule, the second conductor is pulled...

magnetic field of a current loop

Field Along the Axis of a Current Loop

A circular current loop creates a magnetic field along its axis. For a loop of radius a carrying current I, the field at a point P can be found with the Biot-Savart law. The point P lies a distance x from the center of the loop. The field from a tiny current element dl points at an angle θ. At every point on the loop, the current element and the unit vector toward P are perpendicular. Using that relationship and writing r in terms of x and a gives the size of the field from each element. The...

divergence and curl of magnetic field

Magnetic Field Loops and Ampere's Law

Magnetic field loops and Ampere's law describe how magnetic fields behave around current. For a volume current distribution, the magnetic field can be written using the Biot–Savart law. The divergence and curl of that field can then be found with vector analysis. To find the divergence, the divergence operator is applied to both sides of the Biot–Savart equation. After using the vector product rule, the integrand simplifies. The term with the curl of the current density becomes zero because...

ampere's law

Magnetic Circulation Around a Current

Magnetic circulation around a current is described by Ampère’s law. A static magnetic field is not conservative, unlike an electrostatic field. Instead, the magnetic field is linked to electric current, which is its source. Ampère’s law uses the line integral of the magnetic field around a closed path. This integral is proportional to the current enclosed by the loop. The law applies only when currents are steady and when no magnetic materials or time-varying electric fields are present. The...

ampere's law: problem-solving

Choosing an Amperian Loop for Magnetic Fields

Ampere's law connects a closed loop path with the current enclosed by that loop. The line integral of the magnetic field around the path equals the vacuum permeability times the enclosed current. A right-hand rule helps set the sign of the current. If the fingers curl with the integration path, the thumb gives positive current. Current opposite the thumb direction is negative. Solving magnetic field problems with Ampere's law starts by checking symmetry in the current distribution. If the...

solenoids

Solenoids as Controllable Electromagnets

A solenoid is a tightly wound coil of insulated conducting wire. It acts as an electromagnet, and its magnetic field comes from the combined field of each turn in the coil. In an ideal solenoid, the magnetic field inside is almost uniform and points along the solenoid axis. The magnetic field outside is nearly zero. Each turn can be treated as a circular current-carrying loop, and each loop creates a magnetic dipole moment. The dipole moment from one turn equals the current multiplied by the...

magnetic field of a solenoid

Solenoid Field Strength Example

A solenoid is a conducting wire coated with an insulating material and wound tightly into a helical coil. Its magnetic field comes from the vector sum of the fields from each turn. For an ideal solenoid, the field inside depends directly on the number of turns per unit length and the current. The magnetic field outside an ideal solenoid is zero. In this example, a solenoid has 100 turns wrapped around a cylinder that is 1 cm in diameter and 10 cm long. A current of 0.5 A is passed through the...

toroids

Toroid Magnetic Fields and Turn Count

A toroid is a donut-shaped coil made from a single conducting wire. It usually has many circular loops that sit perpendicular to its axis. When current flows through it, the magnetic field forms circular lines around the axis. The right-hand rule shows the field direction: curl the fingers of your right hand with the current, and your thumb points in the magnetic field direction. Inside a toroid, the magnetic field changes with distance from the axis. It varies inversely with that distance.

magnetic vector potential

Solenoid Vector Potential Explained

The magnetic vector potential can be used to describe the magnetic field inside an ideal solenoid. In magnetostatics, the magnetic field has zero divergence, so it can be written as the curl of a vector potential. This idea connects the magnetic field to a potential in the same way that electrostatics connects the electric field to an electric potential. For an ideal solenoid, the magnetic field inside is given by the vacuum permeability, the number of turns per unit length, and the current.

potential due to a magnetized object

Magnetization and Bound Currents

Magnetization describes how a magnetic material responds to an external magnetic field. In paramagnets and ferromagnets, magnetic dipoles align with the field. In diamagnets, the dipoles align opposite to the field. Magnetization is the dipole moment per unit volume, and it plays a role similar to polarization in electrostatics. The magnetic vector potential of a magnetized material can be written in terms of its aligned dipoles. This form is simplified with vector analysis. One term...

magnetostatic boundary conditions

Magnetic Fields at Material Interfaces

Magnetic fields change at the boundary between two magnetic materials, and the change depends on the surface conditions at the interface. A magnetic field can be discontinuous at a surface current, just as an electric field can change across a surface charge. The component of the magnetic field that points perpendicular to the boundary stays continuous. The component parallel to the boundary behaves differently. It becomes discontinuous by an amount equal to the vacuum permeability times the...

ampere's law in matter

Free Current and Magnetization in Ampere’s Law

Ampere’s law in matter links magnetic fields to the free current in a magnetized material. In such materials, the total current density has two parts. These are the free current density and the bound current density. The free current comes from the motion of free electrons inside the material. The bound current comes from the alignment of magnetic dipole moments. In vacuum, the differential form of Ampere’s law says that the curl of the magnetic field equals permeability times current density.

magnetic susceptibility and permeability

How Materials Respond to Magnetic Fields

Magnetic susceptibility and permeability describe how materials respond to a magnetic field. In linear magnetic materials, magnetization is proportional to the magnetic field intensity. The proportionality constant is magnetic susceptibility, which is a dimensionless number. The value of susceptibility depends on the material. Diamagnetic materials develop moments opposite to the applied field. Their susceptibility is slightly negative, usually about 10^-5 to 10^-6. This effect comes from the...

magnetic moment of an electron

Electron Spin and Bohr Magneton

Electrons create magnetic effects through both orbital motion and spin. When an electron moves around a nucleus, it acts like a tiny current loop. That current produces a magnetic dipole moment that is proportional to the electron's orbital angular momentum. The orbital angular momentum is quantized in units of the reduced Planck's constant. Because of that, the magnetic dipole moment is also quantized in the Bohr magneton. The Bohr magneton has a value of 9.27 x 10 -24 Am 2. Electrons also...

diamagnetism

Diamagnetism and Magnetic Repulsion

Diamagnetism is the magnetic response of materials that are repelled by an external magnetic field. These materials contain paired electrons, so they have no net magnetic moment at first. When a magnetic field is applied, moments opposite to the field are induced. Anton Brugmans discovered this effect in 1778 after observing that bismuth is repelled by magnetic fields. He used this observation to suggest that diamagnets are pushed away from magnets. In a non-uniform magnetic field, diamagnets...

paramagnetism

Paramagnetism and Magnetic Alignment

Paramagnetism and magnetic alignment explain how some materials respond to an outside magnetic field. Paramagnets contain unpaired electrons, so they have a finite magnetic moment. When no magnetic field is present, these moments point in random directions, and the net moment is zero. When an external field is applied, a torque acts on the magnetic moments and pulls them toward the field direction. At the same time, thermal motion of the electrons creates a competing torque that tries to...

ferromagnetism

Magnetic Domains and Hysteresis

Ferromagnetic materials like iron, nickel, and cobalt contain magnetic domains. Inside each domain, magnetic dipoles line up in the same direction. Quantum mechanical coupling keeps this alignment strong, so room-temperature thermal motion usually cannot break it. As a result, each domain has a net dipole moment. Some materials have weaker coupling and become ferromagnetic only at lower temperatures. When an external magnetic field is applied, the dipoles rotate to match the field. At the same...

key terms and concepts

Learn how a moving point charge creates a magnetic field, why its direction is perpendicular to the motion plane, and how velocity and angle affect its strength.

Magnetic Fields from Charges 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.5.1

Pennsylvania State Academic Standards

Forces and Interactions

3.2.9-12.L

3.2.9-12.M

Structure and Properties of Matter

3.2.9-12.A

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.d

PH.7

PH.7.a

PH.7.b

Minnesota Academic Standards in Science

Chemistry

4.2.2 9C.3.2.2.1

Arizona Science Standards

HS+Phy.P2

HS+Phy.P2U1.1

Next Generation Science Standards

Energy

HS-PS3-5

new-york-state-science-learning-standards

New York State Science Learning Standards

HS. Energy

HS-PS3-5.

Georgia Standards of Excellence

SPS10.

Electromagnetism

SP5.

relationship-between-electric-currents-and-magnetic-fields

Relationship between Electric Currents and Magnetic Fields.

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). ...

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

Motion Of A Charged Particle In A Magnetic Field

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

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 ...

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.

Magnetic Fields from Charges in Motion

Description

Transcript

Tags

More videos by Standards