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.
Understanding Physics: Faraday's Law of Induction
Magnetic flux is a way to track how much magnetic field passes through a chosen surface. A loop does not need to be physically filled in. Physicists imagine a flat sheet stretched across it, then count the field passing through that sheet.
The field has the greatest effect when it points straight through the loop. It has no flux through the loop when it runs parallel to the sheet. This is why rotating a coil can produce a repeating voltage.
During one turn, the coil moves from maximum flux to zero flux, then to maximum flux in the opposite direction. The induced voltage reverses direction during the rotation, producing alternating current.
The source of the induced voltage is the force on charges in the wire. In a moving conductor, free electrons experience a magnetic force and shift toward one end of the wire. This separation of charge creates a voltage.
In a stationary loop near a changing magnetic field, the changing field creates an electric field that pushes charges around the loop. The loop can therefore have an induced voltage even when no part of the wire is moving.
Voltage exists around the circuit, but current only flows if there is a complete conducting path. A broken loop can still have a measurable voltage across its gap.
The opposition described by Lenz's law is important because it protects conservation of energy. Suppose a magnet is pushed toward a conducting coil. The coil produces a magnetic effect that resists the approach.
A person must do extra mechanical work to keep pushing. That supplied energy becomes electrical energy in the circuit, then perhaps heat in a resistor or motion in a motor. If the induced current helped the magnet move without any work being done, energy would appear from nowhere.
When finding current direction, first decide whether the original flux is increasing or decreasing. Then choose the induced magnetic field that opposes that change. The right hand grip rule can then link the induced field direction to the direction of conventional current.
Generators use this energy transfer on a large scale. Turbines turned by wind, falling water, steam, or engines rotate coils or magnets. Faster rotation usually causes a greater voltage because the flux changes more rapidly.
Transformers use two nearby coils instead of moving parts. An alternating current in the first coil creates a changing magnetic field, which induces a voltage in the second coil.
This allows electrical energy to be sent at high voltage through power lines and changed to safer voltages for homes. Wireless chargers use related ideas, though distance, coil alignment, and unwanted heating reduce efficiency.
Experiments can make the main ideas clear. Connect a coil to a sensitive meter and move a bar magnet toward it, then hold it still, then pull it away. The meter deflects only while the flux is changing, and its direction reverses when the motion reverses.
Try changing the speed, the magnet pole, the coil angle, or the number of turns. Watch for a common mistake. A strong magnetic field alone does not guarantee an induced voltage.
What matters is the rate at which the flux through the loop changes. Keep track of field direction, loop orientation, and the time taken for each change.
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.