Faraday's Law Explained

Faraday's Law

• Michael Faraday discovered that the magnitude of induced Electromotive Force (EMF) in a circuit aligns with the rate of magnetic flux change.
• The average EMF induced is described by the equation: E = -N (ΔB/Δt)

Key Components of the Formula

• E represents the Electromotive Force.
• The negative sign indicates the effect of Lenz's law.
• N stands for the number of turns in the circuit.
• ΔB signifies the rate of magnetic flux change.
• Δt denotes the time interval.

Faraday's Law Variations

• Any change in the magnetic environment around a coil of wire induces a voltage (EMF) irrespective of how the change happens.
• The change can occur by varying magnetic field strength, magnet movement, coil movement, or rotating the coil relative to a magnet.
• Motional EMF appears when a coil moves into a magnetic field that relates to the speed the coil moves into the magnetic field.
• The speed is directly proportional to the rate the coil moves into the magnetic field.

Lenz's Law

• Lenz's Law dictates that when an EMF is produced by a change in magnetic flux its polarity will create a current whose magnetic field opposes the initial change.
• Any induced magnetic field always tries to maintain stability and is illustrated by the examples of the B field increasing or decreasing.

Electromagnetic Induction

• Electromotive force develops with relative motion between a magnetic field and a conductor, and the EMF in generators/inductors is driven by how the magnetic field and conductor work together.

How to Increase Induced EMF

• Increase the magnetic field strength
• Increase the rate of change of flux or the conductor's movement.
• Increase the amount of conductor turns being cut by the magnetic flux, as the induced EMF is proportional to the conductor's length in the magnetic field.

Magnetic Fields that are Created by Current

• Magnetic field lines around a wire with electric current form concentric circles.
• Magnetic strength is proportional to the amount of current.
• The direction of the magnetic field is perpendicular to the wire, matching fingers curled around the wire when the thumb points in the electron flow direction.
• For conventional current flow, use the right hand, however electron flow must be used.

Electromagnetic Induction

• Magnetic field changes when current to a coil is toggled, creating movement between the coil and another nearby conductor.
• Varying current strength in one coil causes expansion of the field that induces voltage in the adjacent secondary conductor.
• The induced voltage direction is opposite the magnetic field from the primary conductor according to Lenz's law.

Self-Inductance

• A straight conductor has inductance, and the surrounding magnetic field changes when current changes.
• Relative motion between magnetic field and conductor induces EMF that is called a self-induced EMF.
• EMF created by the magnetic field is referred to as counter-electromotive force (CEMF).

Back EMF

• Counter-electromotive force polarity opposes the applied voltage, overall working to oppose changes in current.
• CEMF may be known as back EMF.
• Lenz's law says that induced EMF in circuits has to be in the opposite direction of whatever created it.

Inductance

• Inductance is an electrical circuit property that opposes changes in current.
• The symbol for inductance is L, and its basic unit is the henry (H).
• One henry induces one volt in an inductor when current changes by one ampere per second.

Inductors

• Inductance is how a circuit electrical property opposes magnitude changes in current.
• Devices that provide circuit inductance are called inductors (aka chokes, reactors, coils).
• Inductors usually use wire coils, where inductance is from the voltage induced in a conductor.

Inductance Applications

• Radio antenna - radio waves are electromagnetic, so the field induces EMF in the coil.
• Induction stove - changing flux generates EMF in the pot and Power (I2R), as heat, is dissipated in the metal pot, but not in the glass pot because they are insulators.
• Toroid choke - A surge is choked off by the CEMF induced when the magnetic flux changes.

Inductance in AC Circuits

• The conductor can be formed into a loop or coil to increase inductance.
• Current through one loop makes a field that encompasses it so the currents in each loop affect the others.
• The field has the effect of increasing opposition current change.

Inductor Types

• Inductors are classified by core type such as soft iron or air.

Factors that Affect Inductance

• Physical factors affecting inductance include the amount of turns in the coil, its diameter, length, core material, amount of layers.
• Inductance depends on the physical circuit.

Number of Turns and How it Affects Inductance

• The amount of turns in a coil will affect the coils inductance, more turns will increase the inductance exponentially.

Diameter of Coil and How it Affects Inductance

• Constructing a coil with that is a large diameter compared to a small diameter will allow for more lines of force induce CEMF as cross-sectional area of the core increases.

Coil Length and How it Affects Inductance

• A widely spaced coil makes it relatively long, and makes it have few flux linkages and low inductance.
• A coil with closely spaced turns will make it relatively short with high inductance because the close spacing increases flux linkage .
• Doubling the length will halve the value of inductance.

Core Material and How it Affects Inductance

• Using a soft iron core versus coil with an air core will allow for a better path for magnetic lines of force.
• The soft-iron magnetic core has high permeability, and less reluctance to the magnetic flux results in increasing the inductance.

Number of Coil layers and How it Affects Inductance

• Winding coils in layers increases inductance.

Mutual Inductance

• When one conductor’s magnetic flux induces voltage in another separate conductor that is called mutual inductance, where circuits are magnetically linked together.

Factors That Affect Mutual Inductance

• Amount of Turns in each coil
• Physical size of each coil
• Permeability of each coil
• Position of the coils in respect to each other

Factors Increasing Induced EMF

• Magnetic field strength
• Number of conductor turns
• Rate of change of flux (increasing frequency)
• Permeability of core(s)

Primary Current and Induced Voltage

• A Changing magnetic field induces a voltage when the magnetomotive force (MMF) which is the turns multiplied by the current is increased.
• To increase MMF, you can increase the number of turns.
• To increase the current flow To increase the current flow you would have to apply a larger voltage to overcome the CEMF.

Coefficient of Coupling Formula

• M = K√L1 × L2
  • M = mutual inductance in henries
  • K = coefficient of coupling
  • L₁ and L2 = inductance of the coils in henries.

Magnetic Saturation

• When a material is saturated, external magnetisation force will cause internal level magnetisation increase.
• The Hysteresis loop is formed by the changes in magnetising force and the measurements in magnetic flux of the ferromagnetic material.

Terms from the Hysteresis Loop

1. Retentivity is the materials ability to retain residual magnetic field when magnetising force is removed.
2. Residual magnetism or residual flux: This is the magnetic flux level that stays in a material when the magnetizing force is at zero.
3. Coercive refers to the amount of reverse magnetic field that needs that needs to be applied to return magnetic flux back to zero.
4. Material permeability describes how a material easily establishes its magnetic flux.
5. Reluctance is the opposition that shows in a ferromagnetic material for the purpose of establishing a magnetic field.

Series and Parallel Inductors Formulas

• Inductors can be arranged in series or in parallel to achieve the desired results. Induction formulas are similar to calculating resistance.

Voltage/ Current Relationship

• When a switch in inductor/resistor circuit is closed, there is no current because the inductor will (initially) oppose any change,

LR Time Constant Formula

• Time Constant (TC) = L / R
• The time constant depends on the amount of inductance (L) in henrys and the resistance (R) in ohms in the circuit.