The following animation illustrates the principle of the electromagnetic force effect. The animation shows an experimental setup in which a current-carrying conductor is exposed to an external magnetic field. According to the Lorentz force law, a force acts on the conductor. In the animation this force visibly deflects the conductor sideways.
Note on Use
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Description of the Animation
The deflection of the conductor can be explained by the Lorentz force. The Lorentz force acts on a moving charge in a magnetic field.
\[ F = q \cdot v \cdot B \cdot \sin(\theta) \]
q: charge of the electron
v: velocity of the electron
B: strength of the magnetic field,
θ: angle between the direction of movement of the electron and the direction of the magnetic field.
For the setup shown in the animation, the force on the conductor is:
\[ F = B \cdot I \cdot L \cdot \sin(\theta) \]
B: strength of the magnetic field,
I: current in the conductor,
L: length of the conductor in the magnetic field
θ: angle between current direction and magnetic field.
The magnitude and direction of the current can be adjusted using a virtual controller. The resulting magnetic force and the deflection of the conductor update accordingly.
The two-dimensional view can also display the resulting magnetic field, formed by the superposition of the static and dynamic fields.
Note: The animation takes into account the difference between technical and physical current direction. Electrons, indicated by blue spheres, show the physical current direction.
Everyday Applications of the Lorentz Force
The Lorentz force is the operating principle behind many technologies. Whenever a current flows through a conductor inside a magnetic field, a force results. This effect is used in devices found in households, vehicles, and industry.
The electric motor uses the Lorentz force to convert electrical energy into rotational motion. Current flows through a coil positioned between two magnets. The resulting force on the coil creates a torque that drives the rotation.
A loudspeaker works on the same principle. A coil attached to a membrane sits inside a permanent magnet. When an audio signal passes through the coil, the Lorentz force moves the membrane back and forth, producing sound waves.
In maglev trains, electromagnetic forces lift the train above the track and propel it forward. The absence of mechanical contact between train and rail eliminates friction.
Galvanometers and analog measuring instruments also rely on this force. A coil rotates in a magnetic field proportionally to the current flowing through it. The deflection of a pointer indicates the measured value.
Determining the Direction of the Force
The Lorentz force formula gives the magnitude of the force, but not its direction. To determine the direction, physicists use the right hand rule (also called the FBI rule or the three finger rule).
Hold your right hand so that the thumb, index finger, and middle finger point in three perpendicular directions. The thumb points in the direction of the current (technical current direction, from + to −). The index finger points in the direction of the magnetic field (from north to south). The middle finger then points in the direction of the resulting force.
If you reverse the current direction, the force reverses as well. The animation demonstrates this: change the direction of the current using the controller, and the conductor deflects to the opposite side.
Note: The right hand rule applies to the technical current direction. For the physical current direction (electron flow), the left hand rule gives the correct result.
Historical Background
The connection between electricity and magnetism was discovered in 1820 by Hans Christian Ørsted. He observed that a compass needle deflected when placed near a current carrying wire. This was the first evidence that electric currents produce magnetic fields.
André-Marie Ampère built on this discovery. Within weeks of Ørsted’s publication, Ampère showed that two parallel current carrying wires exert forces on each other. He formulated the mathematical relationship between current and magnetic force.
Michael Faraday contributed the concept of field lines and demonstrated electromagnetic induction in 1831. His experiments laid the groundwork for generators and transformers.
Hendrik Antoon Lorentz unified these observations in the 1890s. He formulated the force law that bears his name, describing the force on a charged particle moving through electric and magnetic fields. This formulation remains a cornerstone of electrodynamics.
The Lorentz Force Compared to Other Electromagnetic Phenomena
The Lorentz force is sometimes confused with other electromagnetic effects. A clear distinction helps to avoid misunderstandings.
Lorentz force vs. Coulomb force: The Coulomb force acts between stationary electric charges. It depends on the magnitude of the charges and their distance. The Lorentz force, by contrast, requires a moving charge and a magnetic field. Without motion, no magnetic force acts.
Lorentz force vs. electromagnetic induction: Induction describes the generation of a voltage in a conductor that moves through a magnetic field or is exposed to a changing magnetic field. The Lorentz force describes the force on a current carrying conductor in a static magnetic field. Both phenomena are related but describe different situations.
Lorentz force vs. the force between magnets: Two permanent magnets attract or repel each other due to the alignment of atomic magnetic moments. The Lorentz force specifically describes the interaction between a current and an external magnetic field.
Worked Example
A straight conductor of length L = 0.20 m carries a current of I = 5 A. The conductor is placed perpendicular to a magnetic field of strength B = 0.30 T. What force acts on the conductor?
Since the conductor is perpendicular to the field, the angle θ = 90° and sin(90°) = 1. The formula simplifies to:
\[ F = B \cdot I \cdot L = 0.30 \, \text{T} \cdot 5 \, \text{A} \cdot 0.20 \, \text{m} = 0.30 \, \text{N} \]
A force of 0.30 N acts on the conductor. This is comparable to the weight of a 30 g object (about the mass of two AA batteries).
If the angle between the conductor and the field is reduced to 30°, the force decreases:
\[ F = 0.30 \, \text{T} \cdot 5 \, \text{A} \cdot 0.20 \, \text{m} \cdot \sin(30°) = 0.15 \, \text{N} \]
At 30° the force is halved. At 0° (conductor parallel to the field), the force is zero. The animation allows you to observe how the angle between the field and the current affects the deflection.
From Conductor to Electric Motor
The force on a single conductor, as shown in the animation, is the operating principle of every electric motor. In a motor, the straight conductor is replaced by a coil that can rotate freely between two magnets.
When current flows through the coil, the Lorentz force pushes one side of the coil upward and the other side downward. This creates a torque that causes the coil to rotate. A commutator reverses the current direction every half turn, so the torque continues in the same rotational direction.
The torque of the motor increases with the magnetic field strength, the current, the number of turns in the coil, and the area of the coil. These are the same parameters that determine the Lorentz force on a single conductor.
Modern electric motors use multiple coils arranged at angles to each other. This produces a smoother and more continuous torque. The principle, however, remains the same as the one demonstrated in the animation: a current in a magnetic field produces a force.
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Overview and Download
| Title | Electromagnetic Force on a Conductor |
| Target audience | Teachers and Lecturers |
| Platforms | Microsoft® Windows® Apple® Macintosh® (version dependent) |
| Features | Full screen mode Lossless scaling Large screens and projectors supported |
| License | Freeware |
| Download | Contact |
Contributors
C. Hein, S. Rikowski
Source Information
- 3D engine for 3D model: Papervision3D 2.0
- 3D rotations: Algorithm adopted from Federico Calvo
(http://blog.federicocalvo.com/2009/03/papervision-3d-sphere-globla-axis.html) - Curved field lines: Class Bezier3D by Aleksandar Mancic
- Authoring tool (control elements included): Adobe Animate
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