There’s no standard-level content in this topic. Induction is an additional higher-level treatment of what happens when conductors, magnetic fields and motion are combined.

Flux: how much magnetic field links an area

Magnetic flux density is a vector field quantity that measures the magnetic field passing normally through unit area. It is measured in tesla, where 1 T = 1 Wb m⁻². In earlier work, you may simply have called this magnetic field strength. Here, “flux density” is the more useful term because induction depends on how much field links an area.

Magnetic flux is a scalar quantity that measures the component of a magnetic field passing through a specified area. For a uniform field,

Φ = B**A cos θ, where Φ is magnetic flux (Wb), B is magnetic flux density (T), A is the area linked by the field (m²), and θ is the angle between the magnetic field direction and the normal to the area (rad; degrees are commonly used in this formula).

Don’t use the angle between the field and the plane of the coil unless the question has defined it that way. The formula uses the angle to the normal. If the field goes straight through the face of the coil, θ = 0 and the flux is maximum. If the field lies along the plane of the coil, θ = 90° and the flux is zero.

Field lines are a model, not little strings in space

A helpful picture is to draw magnetic field lines closer together where the field is stronger. More lines through the same drawn area suggests a larger magnetic flux density; more total lines through the area suggests a larger magnetic flux. Treat this as a representation, not a literal count of real lines. This makes a good Nature of Science point: the field-line model works well because it compresses direction and strength into a visual language, but it is still a model.

The unit weber is tied directly to induction. A change of flux of one weber in one second corresponds to an induced emf of one volt in a single turn. That statement will make more sense once Faraday’s law is in place.

What induction actually says

Electromagnetic induction is a process in which a changing magnetic flux linkage produces an emf in a conductor. Induced emf is an energy-per-charge quantity produced by induction that can drive current if a complete conducting circuit is present; it is measured in volts.

One standard demonstration uses a coil connected to a centre-zero galvanometer, with a bar magnet moved towards or away from the coil. The point is not simply that “there is a magnet nearby”. The point is that the flux through the coil is changing. You can make that happen by moving the magnet, moving the coil, changing the field strength, or rotating the coil.

Faraday’s law

In a coil with many turns, each turn adds to the total flux linkage. Magnetic flux linkage is the product of the number of turns and the magnetic flux through each turn. Faraday’s law is

ε = −N ΔΦ / Δt, where ε is the induced emf (V), N is the number of turns in the coil (dimensionless), ΔΦ is the change in magnetic flux through one turn (Wb), and Δt is the time interval over which the change occurs (s).

The size of the induced emf depends on how fast the flux linkage changes. Change the same flux slowly, and the emf is small. Change it quickly, and the emf is larger. On a graph of flux linkage against time, the induced emf is the negative gradient of the graph. A flat section gives no induced emf.

The negative sign matters. It represents Lenz’s law: the induced emf has the direction that opposes the change producing it. We will discuss that energy argument properly in D.4.4.

Ways to produce an induced emf

The syllabus expects you to recognize these examples:

• a time-varying magnetic field, such as a stationary coil near a field that is being switched on, switched off or varied;
• a coil rotating in a uniform magnetic field, the basis of an ac generator;
• relative motion between a conductor and a magnetic field, such as a magnet oscillating near a coil or a coil moving into or out of a magnetic-field region.

Quantitative work is limited to straight conductors moving at right angles to fields, and rectangular coils moving in and out of fields or rotating in fields. That restriction is deliberate: the course is testing the physics of flux change, not awkward three-dimensional geometry.

Self-induction, only qualitatively

Self-induction is an induction effect in which a changing current in a conductor changes the magnetic flux linked with that same conductor, producing an emf that opposes the current change. A coil shows this effect strongly because it links much of its own magnetic field. If the current is increasing, the self-induced emf acts against the increase; if the current is decreasing, it acts to maintain the current. With a steady current, there is no changing flux and therefore no self-induced emf.

No quantitative treatment of inductance, and no resistance–inductor circuit analysis, is required here.

Rate of change as a recurring physics idea

Faraday’s law is another rate-of-change law. The same pattern appears all over physics: velocity is the rate of change of displacement, acceleration is the rate of change of velocity, power is the rate of energy transfer, and radioactive activity is the rate at which nuclei decay. On graphs, “rate of change” usually means “gradient”, so Faraday’s law is a graph-reading idea as well as an equation.

Charge separation in a moving conductor

A metal rod has mobile electrons. When the rod moves through a magnetic field, it carries those charges along with it, and they feel a magnetic force. Electrons are pushed towards one end of the rod, so the other end is left electron-deficient. This charge separation sets up an emf across the rod.

If the rod is isolated, the separated charge quickly creates an electric field inside the rod, which stops any further movement of charge. The induced emf is still there. A continuous current is not, because it needs a complete conducting path.

The motional-emf equation

For a straight conductor moving at right angles to a uniform magnetic field,

ε = BvL, where v is the speed of the conductor perpendicular to the magnetic field (m s⁻¹), and L is the length of the conductor within the magnetic field (m).

This is one of the main quantitative results in the topic. It works neatly for a straight rod cutting a uniform field at 90°. If the conductor does not move at right angles to the field, only the perpendicular component of the motion contributes. In syllabus calculations, though, you are limited to the right-angle case.

Rectangular coils moving into and out of fields

As a rectangular coil enters a uniform magnetic-field region, its flux linkage increases, so an emf is induced. Once the whole coil is fully inside the uniform field and keeps moving without changing its orientation, the flux linkage stays constant and the net induced emf is zero. Students often say “it is cutting field lines, so there must be an emf”. For the whole loop, the emfs on opposite sides cancel when the loop is completely within the same uniform field.

When the coil leaves the field, its flux linkage decreases and the induced emf reverses direction. The magnitude depends on the rate of change of flux linkage: faster motion, more turns, a stronger field, or a larger coil side cutting the boundary all increase the emf.

An everyday example is an aircraft flying through Earth’s magnetic field. Its wingspan can behave like a moving conductor, so a small emf is induced between the wingtips when the motion cuts the vertical component of the field.

Lenz’s law: oppose the change, not necessarily the motion

Lenz’s law is the direction rule saying that an induced emf acts in the direction that opposes the change in magnetic flux linkage that produced it.

The exact wording matters. When a north pole approaches a coil, the near face of the coil becomes a north pole, so it repels the magnet and opposes the increasing flux. When the north pole moves away, the near face becomes a south pole, so it attracts the magnet and opposes the decreasing flux. Either way, the induced effect resists the change.

Why this is conservation of energy

Imagine the induced current helped the change instead. A magnet approaching a coil would be pulled in faster, making a larger change of flux, which would make a larger current and pull the magnet faster again. That would create kinetic energy and electrical energy without any external energy source. Lenz’s law rules out that impossible result.

In a moving-rod generator, when the circuit is closed, the induced current in the rod feels a magnetic force opposite to the rod’s motion. The external agent pulling the rod has to do work against this force. That mechanical work becomes electrical energy in the circuit. If the circuit is open, there can still be an emf but no continuous current, so there is no magnetic braking force associated with an induced current.

This is why a bicycle dynamo turns easily when the lamp circuit is open, but takes more effort when the lamp is lit. The extra effort is not some mysterious loss; it is the mechanical input needed for electrical output.

Links to earlier field ideas

The force on charges in the moving conductor comes from the same magnetic-force idea that can make a charged particle move in a circular path: a force perpendicular to velocity changes the direction of motion. By measuring the radius of a charged particle’s path in a magnetic field, we can find out the particle’s charge-to-mass character, which is why field methods are so useful for identifying particles. In induction, the same family of ideas comes back through Lenz’s law: fields exert forces, forces transfer energy, and energy is conserved.

The same point about representation applies to electric and magnetic fields. Field lines and flux diagrams help us show invisible field properties, but they are still models. Good physicists use the model, and they know its limits.

Why a rotating coil gives alternating emf

An alternating current generator uses electromagnetic induction to produce an emf that reverses direction periodically. It needs a coil, a magnetic field, relative rotation between the coil and field, plus connections so charge can flow in an external circuit.

As the coil turns, the angle between the coil’s normal and the field keeps changing. The magnetic flux linkage changes with it. When the flux linkage is maximum, its gradient is zero, so the induced emf is zero. When the flux linkage passes through zero, it is changing fastest, so the emf has maximum magnitude.

For a rectangular coil rotating at constant angular speed in a uniform magnetic field, the induced emf is sinusoidal:

ε = NBAω sin(ωt), where ω is the angular speed of rotation (rad s⁻¹) and t is time (s).

So the peak emf is proportional to N, B, A and ω. Written in terms of frequency, the rotation rate is

f = ω / 2π, where f is frequency (Hz).

In a practical ac generator, the coil may rotate in a fixed magnetic field, or the magnetic field may rotate around a fixed coil. The physics doesn’t change: the key idea is the changing flux linkage. In a rotating-coil design, slip rings and brushes keep contact with the external circuit without twisting the wires.

Generators, power and industrialization

Induction made large-scale electrical generation possible. Mechanical energy from falling water, steam turbines, wind turbines or engines can be transferred to electrical energy by rotating coils or magnetic fields. This was one of the major physics-to-engineering steps behind industrial electrification: energy could be generated centrally, carried by cables, and used far from the original energy source.

The efficiency of electricity generation depends strongly on the source and on the chain of energy transfers before the generator. A hydroelectric station has a different loss chain from a fossil-fuel or nuclear station, where thermal processes and turbines come before the generator stage. In every case, the generator cannot deliver electrical energy unless mechanical energy is supplied to it, and Lenz’s law explains why a loaded generator is harder to turn.

To increase generator output without changing the supply frequency, engineers can increase the number of turns, use a stronger magnetic field, or increase the coil area. Spinning the generator faster increases the emf, but it also changes the frequency of the alternating supply, which is usually not acceptable for a grid.