1. Concept Overview
Induced emf is the voltage that appears in a conductor whenever the magnetic flux linked with it changes. It is the core idea behind generators, transformers and many electrical devices. What I find interesting is that the emf appears without any battery — it is created purely because of changing magnetic conditions around the conductor.
The moment the magnetic flux starts changing, an induced emf is produced. If the loop is closed, this emf drives an induced current.
1.1. Idea I always keep in mind
Changing magnetic flux → induced emf.
No change in flux means no induced emf, even if a strong magnetic field is present.
2. What Exactly Is Induced EMF?
Induced emf is the electromotive force produced in a conductor due to a change in magnetic flux linked with it. Unlike a battery, it is temporary and appears only while the flux is changing.
I like to think of it as nature's way of resisting changes in magnetic surroundings.
2.1. Relationship with magnetic flux
The induced emf depends on how quickly the flux changes. The mathematical form (from Faraday’s second law) is:
\( \varepsilon = -\dfrac{d\Phi_B}{dt} \)
The negative sign comes from Lenz’s law, showing opposition to flux change.
3. How Magnetic Flux Produces EMF
Magnetic flux through a loop is given by:
\( \Phi_B = B A \cos\theta \)
So whenever any of these — \(B\), \(A\), or \(\theta\) — changes with time, the flux changes and an emf is induced.
3.1. Three ways flux can change
- Change in magnetic field strength: moving a magnet toward or away from a coil.
- Change in area: a sliding conductor increasing or decreasing the enclosed area.
- Change in orientation: rotating a coil in a magnetic field.
4. Factors Affecting the Magnitude of Induced EMF
The induced emf increases when the flux changes more rapidly or when more turns are involved. These are the two major factors that I always note down.
4.1. 1. Rate of change of magnetic flux
The faster the flux changes, the larger the induced emf. Mathematically:
\( \varepsilon \propto \dfrac{d\Phi_B}{dt} \)
This explains why rapidly moving magnets or fast-rotating coils generate stronger emf.
4.2. 2. Number of turns in the coil
A coil with more turns has greater induced emf because each turn experiences the same change in flux. The expression becomes:
\( \varepsilon = -N \dfrac{d\Phi_B}{dt} \)
where \(N\) is the number of turns.
5. Instantaneous and Average EMF
Induced emf can be considered at a specific moment or over a period of time. This depends on whether flux changes smoothly or in steps.
5.1. Instantaneous emf
Used when flux changes continuously or irregularly:
\( \varepsilon = -\dfrac{d\Phi_B}{dt} \)
5.2. Average emf
Used when flux changes uniformly over a time interval:
\( \varepsilon = -\dfrac{\Delta \Phi_B}{\Delta t} \)
6. Role of Lenz’s Law in Induced EMF
Lenz’s law tells me the direction of the induced emf. It states that the induced emf acts in such a way that it opposes the change in flux that produced it.
This opposition is essential to conserve energy — otherwise the induction process would create energy out of nowhere.
6.1. Opposition example
When a magnet is pushed into a coil, the coil produces an induced magnetic field that pushes back. This opposing action is exactly what the negative sign in Faraday's law represents.
7. Physical Feel of Induced EMF
Induced emf is not just theoretical — it can be felt physically. Whenever I try to move a magnet quickly inside a coil, I feel a resistance. This resistance comes from the induced current creating its own magnetic field to oppose the motion.
7.1. Examples emphasising the physical feel
- A magnet falling slowly through a copper tube because induced currents oppose the fall.
- Harder movement of a conductor sliding in a magnetic field due to induced opposing forces.
- Resistance felt when rotating coils in generators.
8. Real-Life Applications
Induced emf is the working principle behind many practical devices. The idea that electricity can be generated by changing magnetic fields forms the basis of modern electrical technology.
8.1. Generators
Rotating a coil in a magnetic field changes flux continuously, generating alternating emf.
8.2. Transformers
Alternating current changes flux in the primary coil, inducing emf in the secondary coil.
8.3. Induction motors and induction cookers
Both work on the idea of changing flux inducing currents in nearby conductors.