AP Syllabus focus: 'Faraday’s law describes the relationship between changing magnetic flux and the resulting induced emf in a system.'
Faraday’s law explains how a changing magnetic environment can create a voltage in a loop or coil. This idea connects magnetism to electricity and underlies many devices that generate electrical energy.
Core idea
Faraday’s law applies to loops, coils, and conducting systems in which the magnetic influence through the system can vary. A steady magnetic field by itself is not enough. What matters is whether the magnetic flux through the chosen system changes with time.
The key quantity is magnetic flux.
Magnetic flux: A measure of how much magnetic field passes through a chosen surface or loop.
Magnetic flux lets physicists describe how much of a magnetic field passes through a chosen surface.
A uniform magnetic field passes through a surface of area ; the flux is maximized when the surface’s area vector (normal) is parallel or antiparallel to . This diagram helps students remember that changing orientation changes the component of through the surface, and therefore changes . Source
If the field strength changes, the size of the enclosed area changes, or the orientation changes, then the flux can change.
The electrical response produced by that change is called induced emf.
A bar magnet moving relative to a wire loop produces a transient induced emf, indicated by the galvanometer deflection. Reversing the magnet’s motion (or swapping which pole approaches the loop) reverses the direction of the induced current, matching the sign change implied by Faraday’s law. Source
Induced emf: A voltage generated by a changing magnetic flux through a system.
Although emf stands for electromotive force, it is a voltage, not a mechanical force. In a closed conducting path, this voltage can drive current. In an open circuit, charge can still separate and produce a measurable potential difference even without continuous current.
Faraday’s law
Faraday’s law gives the quantitative relationship between changing magnetic flux and the induced emf. In AP Physics 2 Algebra, the law is usually applied over a finite time interval for a loop or coil.
= induced emf, in volts
= number of turns in the loop or coil
= change in magnetic flux, in webers
= time interval, in seconds
This expression gives the average induced emf during the chosen time interval.
The larger the change in flux during a given time, the larger the induced emf. If the same flux change happens in less time, the induced emf is greater.
The factor shows that each turn of a coil experiences the changing flux, so the total induced emf increases with the number of turns. If all turns are identical, doubling doubles the induced emf.
The negative sign is part of the full law. It shows that the induced emf is associated with opposition to the flux change, while the detailed direction rule is handled separately by Lenz’s law.
What actually causes induced emf?
Any process that changes magnetic flux through a system can produce induction. Different physical situations can therefore lead to the same basic result.
the magnetic field through the system changes
the system moves so different parts of a field pass through it
the area enclosed by the system changes
the system rotates so its orientation relative to the field changes
These situations may look different, but Faraday’s law treats them in the same way: each one changes magnetic flux.
A common mistake is to focus only on whether a magnetic field is present. A strong field with constant flux produces no induced emf. A weaker field that changes quickly can produce a larger induced emf.
Choosing the system
Faraday’s law is always applied to a specific system, such as a loop, coil, or conducting path. The flux change is considered through the area associated with that chosen path.
In many AP problems, the system is simply the wire loop itself. The law does not require some special kind of motion or a battery. It only requires that the magnetic flux through the chosen system change with time.
It is also important to separate zero flux from zero induced emf. A system can have zero flux at an instant but still have induced emf if the flux is changing at that instant. A system can also have large flux but zero induced emf if that flux stays constant.
Rate of change and system response
Faraday’s law depends on change over time, so induced emf is linked to the rate of change of flux, not just to the amount of flux present. Two systems can have the same total flux change, but the one with the shorter time interval has the larger induced emf.
This is why rapid motion, fast rotation, or quickly changing field conditions tend to produce stronger induction than slow change.
It is also important to separate emf from current. Faraday’s law tells you how much voltage is induced by the changing flux. Whether that voltage produces a large or small current depends on the rest of the circuit, not only on the flux change itself.
In AP questions, qualitative comparisons are often as important as numerical calculations.
Useful reasoning patterns
If , then the induced emf is zero.
A larger in the same time interval gives a larger induced emf.
The same flux change in a shorter time gives a larger induced emf.
Increasing the number of turns increases the induced emf.
Reversing the way the flux changes reverses the sign of the induced emf.
FAQ
Faraday’s law gives $|\mathcal{E}|=\dfrac{|\Delta \Phi_B|}{\Delta t}$ for one turn.
Rearranging gives $|\Delta \Phi_B|=|\mathcal{E}|\Delta t$, so the unit of magnetic flux must be volt-second.
That is why
$1\ Wb = 1\ V\cdot s$
This unit connection is useful because it shows flux is directly tied to how much voltage can be induced over a time interval.
In AP Physics 2 Algebra, Faraday’s law is usually used over a finite time interval, so it gives an average induced emf.
If the flux changes nonuniformly, the induced emf may vary from moment to moment. In a more advanced course, the instantaneous emf is written using a rate at a single instant, not over a time interval.
So the algebra-based form is best understood as:
change over some measured time
giving the average emf during that time
Yes. Faraday’s law is still valid.
What changes is how the flux must be determined. If different parts of the loop experience different magnetic field strengths or directions, the total flux is found by combining the contributions across the whole surface.
In AP-level problems, this is often simplified by:
giving the total flux directly
using regions with simple geometry
treating the field as approximately uniform over the relevant area
The law itself does not require a uniform field.
Many turns increase the induced emf because each turn contributes to the total effect.
Using many turns can also make a device more practical because it allows:
a larger voltage without requiring an extreme flux change
a more compact design
better control of output in coils and generators
A single loop can show induction clearly, but multiple turns make the effect much easier to use in real devices.
Faraday’s law does not create energy from nothing. It describes how a changing magnetic flux produces emf.
If that emf drives current, energy must come from somewhere else, such as:
mechanical work done to rotate a coil
electrical energy used to change a magnetic field
external work done moving a conductor
The induced emf tells you how energy is transferred into electrical form. The total process still obeys conservation of energy.
Practice Questions
The magnetic flux through a single loop changes from to in . Calculate the magnitude of the induced emf.
1 mark for using
1 mark for
A coil has turns. The magnetic flux through each turn decreases uniformly from to in .
(a) Calculate the magnitude of the average induced emf.
(b) A second coil has turns and experiences the same flux change per turn in . Compare the average induced emf of the second coil to that of the first.
(a)
1 mark for finding the flux change per turn:
1 mark for correct substitution into
1 mark for correct answer:
(b)
1 mark for correct proportional reasoning: the second coil has twice the turns but also twice the time interval, so the factors cancel
1 mark for correct comparison: the second coil has the same average induced emf as the first,
