Electromagnetic induction explains how changing magnetic fields create electric fields and currents. This topic connects generators, transformers, motors, wireless charging, and many modern power systems. A cheat sheet helps students keep track of sign conventions, units, and formulas that often look similar but mean different things.
It is especially useful for comparing DC circuit ideas with AC circuits that change over time.
The core ideas include magnetic flux, induced emf, Lenz’s law, and the behavior of inductors and capacitors in alternating current. Faraday’s law states that a changing magnetic flux produces an emf, while Lenz’s law gives the direction of the induced current. In AC circuits, resistance, inductive reactance, and capacitive reactance combine into impedance.
Power in AC circuits depends on rms values and the phase angle between voltage and current.
Key Facts
- Magnetic flux is , where is magnetic field, is area, and is the angle between and the area vector.
- Faraday’s law is , where is the number of loops and the negative sign shows Lenz’s law.
- Motional emf for a straight conductor moving perpendicular to a magnetic field is .
- Self-induced emf in an inductor is , where is inductance in henrys.
- For a transformer, and, for an ideal transformer, .
- The rms values for sinusoidal AC are and .
- Inductive reactance is , and capacitive reactance is .
- The impedance of a series RLC circuit is , and resonance occurs when .
Vocabulary
- Magnetic flux
- Magnetic flux is the amount of magnetic field passing through an area, calculated by .
- Induced emf
- Induced emf is the voltage produced when magnetic flux through a circuit changes over time.
- Lenz’s law
- Lenz’s law states that an induced current flows in a direction that opposes the change in magnetic flux that caused it.
- Inductance
- Inductance is a property of a coil or circuit that measures how strongly it opposes changes in current.
- Reactance
- Reactance is the opposition to AC current caused by inductors or capacitors, measured in ohms.
- Impedance
- Impedance is the total opposition to AC current in a circuit, combining resistance and reactance.
Common Mistakes to Avoid
- Dropping the negative sign in Faraday’s law is a mistake because includes Lenz’s law, which determines the direction of the induced effect.
- Using for magnetic flux without is a mistake because flux depends on the angle between the magnetic field and the area vector.
- Confusing peak and rms values is a mistake because AC power calculations usually use and , not and .
- Adding resistance and reactance directly in a series RLC circuit is a mistake because impedance uses , not .
- Assuming a transformer changes power in an ideal circuit is a mistake because an ideal transformer has , so increasing voltage decreases current.
Practice Questions
- 1 A coil with turns has its magnetic flux change from to in . Find the average induced emf.
- 2 A transformer has turns and turns. If the primary voltage is , what is the secondary voltage for an ideal transformer?
- 3 In a series RLC circuit, , , and . Calculate the impedance .
- 4 Explain why an induced current appears in a loop when a magnet is pushed toward it, and describe how Lenz’s law determines the current’s direction.
Understanding Electromagnetic Induction and AC Circuits
Induction depends on change, not simply on the presence of a magnetic field. A wire loop sitting still in a steady field has no sustained induced voltage. The situation changes when the magnet moves, the loop moves, the loop turns, its area changes, or the field strength changes.
A generator uses continuous rotation so that the amount of field passing through each coil rises, falls, and reverses regularly. More coil turns produce a larger induced voltage because each turn contributes.
Faster rotation produces a higher frequency and usually a larger voltage. This is why the speed of a generator matters.
Lenz’s law is really an energy rule. The induced current creates a magnetic effect that opposes the change that caused it. If a moving magnet approaches a coil, the coil resists that approach.
Someone moving the magnet must do work. That mechanical work becomes electrical energy, often followed by heat or light in a circuit. Without this opposition, a system could create energy from nothing.
Inductors show the same principle in circuits. They resist rapid changes in current because a changing current changes their own magnetic field.
When current is switched off, an inductor can produce a large voltage. This causes sparks in relays and switches, so protective components are often used.
In AC circuits, current does not always reach its maximum at the same time as voltage. A resistor has voltage and current in step, and it turns electrical energy into thermal energy. An inductor makes current lag behind voltage because it stores energy temporarily in a magnetic field.
A capacitor makes current lead voltage because it stores energy in an electric field. Reactance describes how strongly an inductor or capacitor limits AC current. Inductive reactance increases as frequency increases.
Capacitive reactance decreases as frequency increases. At resonance in a series circuit, the opposing timing effects of the inductor and capacitor cancel.
The impedance can then become small, making the current large. Resonance is useful for tuning radios, though it can damage equipment if current is not limited.
Transformers use induction to change voltage levels without direct electrical contact between the coils. They need a changing current in the primary coil, which is why ordinary transformers do not work with steady DC. Power stations raise voltage before long distance transmission.
For a given power, higher voltage means lower current. Lower current reduces energy lost as heating in power lines. At homes and schools, meters and appliance labels use rms voltage and current.
These values describe the heating effect of AC in the same practical way as equivalent DC values. When solving problems, track units carefully, identify the frequency, and decide whether the circuit behavior is mainly resistive, inductive, or capacitive before choosing a formula.