The following animation illustrates the principle of electromagnetic induction. A conductor is moved through a magnetic field, with the induced voltage displayed in real time.
What Is Electromagnetic Induction?
Electromagnetic induction is one of the most important phenomena in physics: a voltage is produced whenever a conductor and a magnetic field move relative to each other. No battery or other voltage source is needed – the motion itself generates the voltage.
The basic formula for the induced voltage is:
\[ U = B \cdot l \cdot v \]
Here, \( B \) is the magnetic flux density (in tesla), \( l \) is the length of the conductor inside the field (in metres) and \( v \) is the velocity of the conductor (in metres per second). The faster the movement or the stronger the field, the higher the induced voltage. Try it in the animation: drag the grey conductor slowly and then quickly through the horseshoe magnet – in the real-time diagram on the right you can see how the voltage peaks are significantly higher with faster movement.
This principle is the foundation of virtually all electrical power generation – from bicycle dynamos to large-scale power plants.
Induction in Everyday Life
Electromagnetic induction is all around us, even when we are not aware of it:
- Bicycle dynamo: A magnet rotates next to a coil – the changing magnetic field induces a voltage that powers the light.
- Wireless charging: A changing magnetic field in the charging pad induces a current in the receiving coil of the smartphone.
- Electric guitar pickups: The vibrating steel string changes the magnetic field around the pickup coil – the induced voltage becomes the audio signal.
- Contactless card readers: When you hold your bank card against the terminal, the reader induces a current in the card’s antenna coil to power the chip.
All of these applications work on the same principle that the animation demonstrates: relative motion between a conductor and a magnetic field produces a voltage.
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Description of the Animation
The horseshoe magnet is colour-coded: the upper pole is red, the lower one green. The magnetic field runs between the poles. Move the grey conductor horizontally through this magnetic field. The current direction is indicated by a red symbol: A dot means “current flowing out of the plane”, a cross means “current flowing into the plane”.
The induced voltage is calculated according to the law of induction:
\[ U = B \cdot l \cdot v \]
- B: Magnetic flux density (strength of the magnetic field) in Tesla (T)
- l: Length of the conductor in the magnetic field in meters (m)
- v: Velocity of the conductor in meters per second (m/s)
This formula applies when the conductor moves perpendicular to the field lines (angle \( \alpha \) = 90°). In the general case:
\[ U = B \cdot l \cdot v \cdot \sin(\alpha) \]
At \( \alpha \) = 90° the formula simplifies to U = B · l · v, since sin(90°) = 1. This corresponds to the case shown in the animation.
To the right of the magnet, a real-time diagram shows the induced voltage U over time t. The curve scrolls continuously from right to left. Positive deflections (upward, towards +U) occur when the conductor moves in one direction, negative deflections (downward, towards −U) when it moves in the opposite direction. When the conductor is stationary, the curve settles on the zero line.
Interactive Controls
The slider in the upper right corner of the animation controls the magnetic field strength B (range: 0.5 to 1). Increase the value and move the conductor again – at the same speed, the voltage peaks in the diagram become larger, exactly as the formula U = B · l · v predicts.
Below the slider there is a checkbox labelled “resultant magnetic field”. Activate it to see the superposition of both magnetic fields. The magnet’s field lines then deform depending on the conductor’s motion.
The Lorentz Force – Why Is a Voltage Produced?
The physical cause of induction can be understood through the Lorentz force. When a conductor is moved through a magnetic field, the free charge carriers (electrons) inside it also move. A charge \( q \) moving with velocity \( v \) through a magnetic field \( B \) experiences the Lorentz force:
\[ F_L = q \cdot v \cdot B \]
- \( F_L \): Lorentz force (in newtons, N)
- \( q \): Electric charge of the carrier (in coulombs, C)
- \( v \): Velocity of the charge carrier (in m/s)
- \( B \): Magnetic flux density (in tesla, T)
This force pushes the electrons towards one end of the conductor and leaves a deficit of negative charge at the other end. The result is a potential difference – the induced voltage. The faster the conductor moves, the greater the Lorentz force on each electron, and the higher the voltage.
The animation makes this directly visible: inside the grey conductor, a red cross appears when you move it to the right (current flowing “into the plane”) and a red dot when you move it to the left (current flowing “out of the plane”). These symbols indicate the direction of electron flow caused by the Lorentz force. Move the conductor quickly – the diagram shows a high voltage peak. Move it slowly and the voltage is small.
Understanding Lenz’s Law
Lenz’s law states that the induced current always flows in such a direction as to oppose the change that caused it. This is a direct consequence of energy conservation.
An example: if you move the conductor to the right through the magnetic field, a current is induced. This current, flowing through the magnetic field, produces a force (the Lorentz force again!) that acts to the left – opposing the motion. You therefore have to do work to keep the conductor moving. That work is exactly the electrical energy that the induced current delivers.
If Lenz’s law did not hold, the induced current would accelerate the conductor instead of braking it – and energy would be created from nothing, violating energy conservation.
You can observe this directly in the animation: drag the conductor to the right – the diagram shows a deflection upward (+U). Then drag it back to the left and the curve dips downward (−U). The sign of the voltage reverses with the direction of movement – exactly as Lenz’s law demands. At the same time, the symbol inside the conductor switches between cross and dot, indicating the reversal of current direction.
The Magnetic Field of the Current-Carrying Conductor
A current-carrying conductor creates its own magnetic field. The field lines form circles around the conductor. The animation shows this field as a circle with arrowheads.
The direction of this field follows the right-hand rule. Point the thumb in the current direction and the fingers indicate the field line direction.
When the conductor moves to the right, current flows into the plane. The field then runs clockwise around the conductor. When the conductor moves to the left, the direction reverses. The arrowheads on the circle then point counterclockwise.
The Resultant Magnetic Field
The checkbox enables the display of the resultant magnetic field. It results from the superposition of the magnet’s field and the conductor’s field.
On one side of the conductor, both fields point in the same direction. The field lines are closer together there. On the other side, the fields oppose each other. The field lines are farther apart there.
This field distribution creates a force on the conductor. It acts from the compressed side toward the spread side. This corresponds to Lenz’s law: the force opposes the motion.
Magnetic Flux and the General Law of Induction
The formula \( U = B \cdot l \cdot v \) is a special case. The general formulation of Faraday’s law uses the concept of magnetic flux \( \Phi \):
\[ \Phi = B \cdot A \]
Here \( A \) is the area of the conductor loop that is penetrated by the magnetic field. The induced voltage equals the rate of change of the magnetic flux:
\[ U = -\frac{d\Phi}{dt} \]
You can see this relationship indirectly in the animation: when the conductor is pulled quickly through the magnet, the area penetrated by the field changes rapidly – dΦ/dt is large, and the diagram shows a high voltage deflection. When the conductor moves slowly, the change in flux is small and so is the voltage.
The minus sign expresses Lenz’s law: the voltage opposes the change. This general law covers all cases of electromagnetic induction – not only a moving conductor, but also a changing magnetic field strength or a changing loop area.
For a coil with \( N \) turns the induced voltage is \( N \) times larger:
\[ U = -N \cdot \frac{d\Phi}{dt} \]
This is why transformers and generators use coils with many turns – each turn contributes the same voltage, and the total adds up.
Physical Background
Electromagnetic induction was discovered by Michael Faraday in 1831. When a conductor passes through a magnetic field (or the field changes around it), a voltage is induced. The direction of the induced voltage follows Lenz’s law – it opposes the cause of its creation.
Faraday’s discovery was a milestone in physics: it revealed that electric and magnetic fields are not independent but are intimately connected. This insight later led James Clerk Maxwell to formulate his famous equations, which unified electricity, magnetism and light into a single theory.
From a technological perspective, induction made the age of electrical power possible. Before Faraday, the only way to produce a continuous current was through chemical batteries. With induction, mechanical energy – from water turbines, steam engines or wind – could be converted into electrical energy on an industrial scale.
Practical Applications
Electromagnetic induction is the basis of countless technologies:
- Generators: A coil rotates in a magnetic field (or a magnet rotates inside a coil). The continuously changing flux induces an alternating voltage. This is how power plants – whether coal, gas, nuclear, hydro or wind – produce electricity.
- Transformers: Two coils share a common iron core. An alternating current in the primary coil creates a changing magnetic flux, which induces a voltage in the secondary coil. The voltage ratio equals the turns ratio: \( U_1 / U_2 = N_1 / N_2 \). This is how the grid steps voltage up for long-distance transmission and back down for household use.
- Induction cooktops: A coil beneath the cooking surface generates a rapidly alternating magnetic field. This induces eddy currents in the ferromagnetic base of the pot, and the electrical resistance of the metal converts them into heat – directly in the cookware, not in the hob itself.
- Eddy current brakes: When a conductive disc or rail passes through a magnetic field, eddy currents are induced that oppose the motion (Lenz’s law). The result is a braking force with no mechanical contact and therefore no wear. These brakes are used in high-speed trains, roller coasters and industrial machinery.
- Inductive sensors: Many speed and position sensors in cars, machines and industrial plants work by detecting the voltage induced when a toothed metal wheel rotates past a coil.
Summary: Key Formulas
| Formula | Meaning | Applies to |
| \( U = B \cdot l \cdot v \) | Induced voltage | Conductor perpendicular to field |
| \( U = B \cdot l \cdot v \cdot \sin(\alpha) \) | Induced voltage (general) | Conductor at angle to field |
| \( F_L = q \cdot v \cdot B \) | Lorentz force | Charge in magnetic field |
| \( \Phi = B \cdot A \) | Magnetic flux | Uniform field through area |
| \( U = -d\Phi / dt \) | Faraday’s law | Any induction process |
| \( U = -N \cdot d\Phi / dt \) | Faraday’s law (coil) | Coil with N turns |
| \( U_1/U_2 = N_1/N_2 \) | Transformer equation | Ideal transformer |
Related Animations
HD Animations
Overview
| Title | Introduction to the Law of Induction |
| Target Audience | Teachers and Lecturers |
| Features | Full-screen mode Lossless scaling Large screens and projectors supported |
| License | MIT |
Contributors
C. Hein, S. Rikowski