Faraday's law of induction explains how electricity can be produced from changing magnetic fields. When the magnetic flux through a loop of wire changes, an electromotive force, or EMF, is induced around the loop. This is the basic physics behind generators, transformers, wireless charging, and many sensors.
The minus sign in the law reminds us that the induced current acts to oppose the change that caused it.
Key Facts
- Faraday's law for a coil: ε = -N ΔΦB / Δt
- Differential form: ε = -N dΦB / dt
- Magnetic flux through a flat loop: ΦB = B A cos θ
- EMF increases when the number of turns N increases.
- EMF increases when magnetic flux changes faster, so a faster moving magnet gives a larger induced voltage.
- Lenz's law gives the direction of induced current: the induced magnetic field opposes the change in flux.
Vocabulary
- Electromotive force
- Electromotive force, or EMF, is the energy supplied per unit charge by induction and is measured in volts.
- Magnetic flux
- Magnetic flux is the amount of magnetic field passing through a surface, calculated as ΦB = B A cos θ for a uniform field.
- Induced current
- Induced current is the current produced in a closed conducting loop when the magnetic flux through it changes.
- Lenz's law
- Lenz's law states that an induced current flows in the direction that opposes the change in magnetic flux.
- Coil turns
- Coil turns are the repeated loops of wire in a coil, and more turns multiply the total induced EMF.
Common Mistakes to Avoid
- Ignoring the minus sign in ε = -N ΔΦB / Δt is wrong because it gives the direction information from Lenz's law, not a negative size for voltage.
- Using magnetic field B instead of magnetic flux ΦB is wrong because induction depends on the field passing through an area at an angle, not just field strength.
- Forgetting the number of turns N is wrong because each loop contributes EMF, so a 100 turn coil can induce 100 times the voltage of one loop under the same flux change.
- Assuming a stationary magnet near a stationary coil always induces current is wrong because induction requires changing magnetic flux, not just the presence of a magnetic field.
Practice Questions
- 1 A 50 turn coil experiences a magnetic flux change from 0.020 Wb to 0.005 Wb in 0.10 s. What is the magnitude of the induced EMF?
- 2 A circular coil has 200 turns and area 0.030 m2. A uniform magnetic field perpendicular to the coil increases from 0.10 T to 0.40 T in 0.50 s. What EMF is induced?
- 3 A bar magnet is pushed north pole first into a coil connected to a galvanometer, then pulled back out. Explain why the needle deflects in opposite directions during the two motions.