Introduction to Electromagnetic Induction

This concept explains how most large-scale electrical energy is generated in power plants. Instead of using a lot of batteries, we rotate coils in magnetic fields (or rotate magnets near coils) to generate electricity continuously. Once I understood this, generators, transformers and many machines started making much more sense.

So for my notes, I keep one line in mind: "Change in magnetic flux → induced emf → possible induced current".

Magnetic flux through a surface is a measure of how much magnetic field is passing through that surface. For a uniform field and flat area, it is given by

\( \Phi_B = B A \cos\theta \)

where \( B \) is magnetic field, \( A \) is area of the loop, and \( \theta \) is the angle between the magnetic field and the normal (perpendicular) to the area.

Induced emf is the emf (electromotive force) produced in a conductor or circuit when the magnetic flux linked with it changes with time. It behaves like a temporary "voltage source" created by changing magnetism.

Induced current is the current that flows in a closed conducting loop because of the induced emf produced by changing magnetic flux.

Electromagnetic induction is the phenomenon in which an emf is induced in a conductor due to a change in magnetic flux linked with it.

The most important point from Faraday’s work that I want to remember:

• Just having a strong magnetic field is not enough.
• Just having a coil is not enough either.
• There must be a change in magnetic flux with time through the coil for induction to happen.

So I write a small note for myself: "No change in flux → no induced emf".

Faraday found that the magnitude of induced emf is related to how fast the magnetic flux changes with time. Faster change in flux means larger induced emf.

In proportional form, I remember it like this:

\( \varepsilon \propto \dfrac{\Delta \Phi_B}{\Delta t} \)

This will later become the mathematical statement of Faraday’s law, usually written as

\( \varepsilon = -\dfrac{\mathrm{d}\Phi_B}{\mathrm{d}t} \)

but at this stage I just keep the idea: rate of change of flux decides the size of induced emf.

If the magnetic field through the loop becomes stronger or weaker with time, the magnetic flux \( \Phi_B \) changes. For example:

• Moving a bar magnet quickly towards or away from a coil.
• Switching an electromagnet on or off near a coil.

If the part of the loop area lying in the magnetic field changes with time, the flux also changes. Example:

• Stretching or squeezing a flexible conducting loop in a magnetic field.
• Sliding a conductor on a U-shaped conductor so that the rectangular area changes.

From the formula \( \Phi_B = B A \cos\theta \), I know that flux also depends on the angle \( \theta \) between the field and the normal to the loop. So if I rotate the loop in a uniform magnetic field, \( \theta \) changes with time and hence \( \Phi_B \) changes.

This is the basic idea behind rotating coil generators.

• When the north pole of a magnet is moved towards the coil, the galvanometer shows a momentary deflection.
• When the magnet is held steady inside the coil, the galvanometer returns to zero.
• When the magnet is moved away from the coil, the galvanometer deflects again but in the opposite direction.

From this, I note:

Deflection only when the magnet is moving, not when it is at rest relative to the coil.

If I keep the magnet fixed and move the coil towards or away from the magnet, I still get induced current. So what really matters is the relative motion and hence the change in magnetic flux, not which object is moving.

Again, no relative motion means no change in flux and hence no induced current.

The induced current always flows in such a direction that its own magnetic effect opposes the change that produced it. This is a very important physical idea: nature resists changes in magnetic flux.

This is why there is a negative sign in the formula

\( \varepsilon = -\dfrac{\mathrm{d}\Phi_B}{\mathrm{d}t} \)

For now, I just remember a short sentence: "Induced current opposes the change in flux".

In a generator, a coil is rotated in a magnetic field (or a magnet is rotated near a coil). Because the orientation of the coil in the magnetic field keeps changing, the magnetic flux \( \Phi_B \) changes continuously. This induces an alternating emf, which gives alternating current used in homes and industries.

In a bicycle dynamo, the wheel rotation turns a small magnet or coil and produces emf to light up the lamp. In an induction cooker, changing currents in a coil create a changing magnetic field, which induces currents in the metal vessel and heats it up.

In some microphones, sound causes a diaphragm and attached coil to move in a magnetic field, changing the flux and inducing a small emf that represents the sound signal. In speakers, changing current in a coil creates changing magnetic forces that move the diaphragm to produce sound.

All these examples are different faces of the same core idea: change in magnetic flux leading to induced emf and current.