Name: current and magnetic field around a wire
Uploaded: 2023-04-30T12:40:55.000Z
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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-a-current-carrying-conductor

Magnetic Force On A Current-Carrying Conductor

Stellen Sie sich einen Kompass vor, der in der Nähe eines stromdurchflossenen Leiters platziert ist. Die Nadel erfährt eine Kraft und wird tangential zu einem Kreis um den Leiter ausgerichtet. So bilden sich konzentrische Schleifen aus Magnetfeldern um den Leiter.
Die Richtung des vom Leiter erzeugten Magnetfeldes lässt sich durch die Rechtsregel bestimmen: Der Daumen zeigt in Richtung des Stroms und die umwickelten Finger geben die Richtung vor.
Wenn sich das Magnetfeld von der Ebene nach außen bewegt, wird es durch einen Punkt dargestellt; bewegt es sich auf die Ebene zu, wird es durch ein Kreuz dargestellt.
Betrachten Sie einen verschwindend kleinen Querschnitt des stromdurchflossenen Leiters in einem gleichmäßigen Magnetfeld. Wenn n die Anzahldichte der freien Ladungen ist, dann kann die Anzahl der Ladungsträger in der Sektion bestimmt werden.
Unter Berücksichtigung der Driftgeschwindigkeitsgleichung können die magnetische Kraft auf eine einzelne Ladung und die gesamte magnetische Kraft im Schnitt bestimmt werden.
Unter der Annahme, dass die Länge des infinitesimalen Abschnitts in die gleiche Richtung wie die Driftgeschwindigkeit verläuft, kann die Kraft auf den stromdurchflossenen Leiter bestimmt werden.

<ol>
	<li>OpenStax. (2019). Universitätsphysik Vol. 2. [Web-Version], Seite 396 - 398. Abgerufen von <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>

magnetische kraft auf einen stromführenden leiter

Bewegte Ladungen erfahren eine Kraft in einem magnetischen Feld. Da die magnetischen Felder, die von bewegten Ladungen erzeugt werden, proportional zum Strom sind, erzeugt ein Leiter, der einen Strom führt, ein magnetisches Feld um sich herum.

Betrachten Sie einen Kompass, der in der Nähe eines stromführenden Drahts platziert ist. Der Draht erfährt eine Kraft, die die Nadel des Kompasses tangential um den Draht ausrichtet. Somit erzeugt der stromführende Draht konzentrische, kreisförmige Schleifen des magnetischen Feldes. Das magnetische Feld, das von einem Draht erzeugt wird, kann mit der Rechte-Hand-Regel bestimmt werden, die besagt, dass die Richtung des magnetischen Feldes gegeben ist, wenn der Daumen in Richtung des Stroms zeigt und die Finger sich um den Draht krümmen. Betrachten Sie eine rechteckige Ebene in Richtung XY. Wenn das magnetische Feld aus der Ebene hinausgeht, werden diese magnetischen Feldlinien durch ein Punkt-Symbol dargestellt. Wenn das magnetische Feld in die Ebene hineingeht, werden diese magnetischen Feldlinien durch ein Kreuz-Symbol dargestellt.

Betrachten Sie einen geraden leitenden Draht mit einem Strom, der von unten nach oben fließt und eine Länge l sowie einen Querschnittsbereich A hat. Der leitende Draht wird in einem einheitlichen magnetischen Feld platziert, das senkrecht zur Ebene steht und in die Ebene gerichtet ist. Die Driftgeschwindigkeit wirkt nach oben und steht senkrecht zum magnetischen Feld. Die durchschnittliche Kraft auf jede Ladung ist nach links gerichtet und wird wie folgt angegeben:

<img alt="Equation1" src="/files/ftp_upload/13768/13768_Equation_1.svg" style="text-align: center; height: 22px;" />

Wenn es n Ladungen pro Einheitsvolumen gibt, dann ergibt sich das Produkt aus dem Querschnittsbereich des Drahtes, der Anzahl der Ladungen pro Einheitsvolumen und der Länge das Volumen des segmentierten Drahtes. Somit hat die gesamte magnetische Kraft auf das Segment eine Größenordnung von:

<img alt="Equation2" src="/files/ftp_upload/13768/13768_Equation_2.svg" style="text-align: center; height: 14px;" />

Durch Erinnerung an die Gleichung für die Driftgeschwindigkeit und das Einsetzen der Begriffe kann die Gesamtkraft auf das Segment wie folgt berechnet werden:

<img alt="Equation3" src="/files/ftp_upload/13768/13768_Equation_3.svg" style="text-align: center; height: 12px;" />

Magnetische Kraft auf einen stromführenden Leiter

Sich bewegende Ladungen erfahren eine Kraft in einem Magnetfeld. Da die durch bewegte Ladungen erzeugten Magnetfelder proportional zum Strom sind, ...

Education

Lehre

JoVE Core

Physics

Physik

Unit 1

Einheit 1

Magnetic Forces and Fields

Magnetische Kräfte und Felder

KEY TERMS AND CONCEPTS

KERNBEGRIFFE UND KONZEPTE

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 the direction of the current, the curled fingers show the direction of the magnetic field around the wire.

Magnetic field lines are also shown with symbols in a plane. A dot symbol means the field points out of the plane, while a cross symbol means the field points into the plane. For a straight conducting wire with current flowing upward, the wire can be placed in a uniform magnetic field directed into the plane.

In that setup, the drift velocity points upward and stays perpendicular to the magnetic field. The average force on each charge points to the left. If the wire segment has length l and cross-sectional area A, then the volume of the segment is found from A times the length, and the total magnetic force on the segment can be written from that charge count. Using the drift velocity equation lets the force be rewritten in a final form.

Current and Magnetic Field Around a Wire

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

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

See how a current-carrying wire creates circular magnetic field lines, how the right-hand rule shows field direction, and how force acts on moving charges.

Current and Magnetic Field Around a Wire | 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

Minnesota Academic Standards in Science

3.1.1 9P.2.2.1.3

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

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New York State Science Learning Standards

HS. Forces and Interactions

HS-PS2-5.

HS. Energy

HS-PS3-5.

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

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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

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Average Acceleration

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Instantaneous Acceleration

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Position and Displacement Vectors

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average-and-instantaneous-velocity-vectors

Average and Instantaneous Velocity Vectors

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Acceleration Vectors

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Direction of Acceleration Vectors

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Linear Momentum

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Force and Momentum

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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

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

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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

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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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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

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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

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

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 ...

Moving charges experience a force in a magnetic field. Since the magnetic fields produced by moving charges are proportional to the current, a conductor ...

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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Consider a point charge moving with a ...

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Magnetic Field Due to Two Straight Wires

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magnetic-force-between-two-parallel-currents

Magnetic Force Between Two Parallel Currents

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Magnetic Field Of A Current Loop

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Divergence and Curl of Magnetic Field

The magnetic field due to a volume current distribution given by the Biot&#8211;Savart Law can be expressed as follows:

To evaluate the divergence of the ...

Ampere's Law

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

Ampere's Law: Problem-Solving

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Solenoids

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Magnetic Field of a Solenoid

A solenoid is a conducting wire coated with an insulating material, wound tightly in the form of a helical coil. The magnetic field due to a solenoid is ...

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.

Current and Magnetic Field Around a Wire

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