Electromagnetic Induction and Transformers

Electromagnetic Induction Overview

• Electromagnetic induction involves how electric and magnetic fields are related
• Magnetic flux can change, relating to Φ = B⊥A = BA cos θ
• Energy transfers and transformations demonstrate Faraday's Law and Lenz's Law with ε = -N(ΔΦ/Δt)
• Electromotive force (EMF) generation and Lenz's Law are evident in relative movement between magnets, conductors, metal plates, and solenoids

Transformer Operation

• Ideal transformers operation can be analyzed quantitatively to discover: Vp/Vs = Np/Ns and VpIp = VsIs
• The ideal transformer model has limitations
  • Incomplete flux linkage
  • Resistive heat production
  • Eddy currents
• Step-up and step-down transformers have applications
  • The distribution of energy utilize high-voltage transmission lines

Michael Faraday's Discoveries

• Michael Faraday (1791–1867) discovered that an electric current produces a magnetic field.
• He found that a current-carrying conductor experiences a force in a magnetic field (the motor effect).
• In August 1831, Faraday discovered electromagnetic induction.
• Electromagnetic induction includes EMF and electric current generation through a magnetic field
• Faraday's work led to modern electrical energy generation methods.

Faraday's Initial Experiments

• Faraday aimed to produce and detect current in a coil by using the magnetic field of another coil.
• He coiled copper wire around a wood block, separated by twine.
• One coil connected to a galvanometer, the other to a battery
• Early efforts failed due to the galvanometer's lack of sensitivity for the experiment
• Closing the battery circuit caused a sudden deflection on the galvanometer, observed as a small, brief current in the secondary circuit
• A similar, opposite effect occurred when the battery circuit was stopped
• Induced currents were temporary and nonexistent with constant battery circuit currents

Improvements to Early Experiments

• Faraday modified the experiment by using a glass tube for the secondary coil, containing a steel needle, he subsequently closed the initial circuit
• Removing the needle, it was found magnetised, showing induced secondary circuit current
• Placing a steel needle in the secondary coil with primary current flowing, then stopping led to reversed needle magnetization

The Iron Ring Experiment

• Faraday used a soft iron ring with primary and secondary coils on opposite sides
• Connecting the primary coil to a battery made the galvanometer needle respond
• The effect was not permanent
• Cutting the current induced the needle to move in the opposite direction
• A current was induced in the secondary coil when the magnetic field of the primary coil was changing

Using A Magnet

• Moving a magnet near a coil can generate electric current, showing the effect of the North pole approaching, halting, and retreating
• Induced current's magnitude relies on the speed at which the magnet approaches or leaves the coil

Magnetic Flux

• Electromagnetic induction involves creating EMF in a conductor moving relative to, or within, a changing magnetic field
• Magnetic fields can be represented with field or flux lines
• Lines show the direction of force on a compass's North pole, with density indicating strength
• Magnetic flux (ΦB) refers to magnetic field amount through an area, measured in webers (Wb)
• If area A is perpendicular to uniform field B: ΦB = BA
• Magnetic field strength (B) indicates the magnetic flux density, measured in tesla (T) or Wb/m²

Faraday's Law of Induction

• To demonstrate current flow within a galvanometer during a Faraday experiment, EMF (ℰ) must be present
• EMF determines the magnitude of current within said Galvanometer.
• A fluctuation within the magnetic current threading (or passing) across galvanometer, determines EMF
• Magnitude, or rate of change, determines EMF measured in time

Lenz's Law

• An induced EMF always results in a current that forms a magnetic field, which resists any shift to flux along a circuit
• This principle derives from the Law of Conservation of Energy
• Faraday's Induction Law incorporates a minus sign to highlight this characteristic

The Field Line Method

• Helpful to determine EMF and direction of current using a field line schematic
• When a magnet shifts direction toward the coil, magnetic flux density within the coil fluctuates, producing a magnetic field, with dotted lines opposing the rate of change
• Field lines point in opposing directions to regulate this directional influence

Eddy Currents

• Eddy currents arise from magnetic fields affecting metal objects: relative movement, conductors moving externally, or changing magnetic fields
• Magnetic fields from eddy currents counteract field changes acting on metal objects
• A rectangular metal sheet being removed from an external magnetic field creates charged particle movement and eddy currents.

Induction Switches

• Metal detectors are commonly implemented at airports and security checkpoints.
• High-frequency oscillator induces alternating current within coil to detect metal using alternating electromagnetic field reaching 22MHZ.
• A metal object in proximity produces eddy currents within oscillating electromagnetic field.
• The metal object adds a load to which ultimately detects alarms in nearby circuits.
• Threshold can be set to detect desired objects from coins and zippers to knifes and guns.

Induction Heating

• Eddy currents lead to increased metal temperature due to moving charges, atom collisions, and magnetic field fluctuations.
• Induction heating effectively heats conducting material through eddy currents caused by changing magnetic fields.
• It is efficiently utilized with induction cookers and furnaces, but not desirable in electrical equipment as it leads to thermal transfer.
• Gas stovetops warm the hot gasses along bottoms of saucepans to transfer heat and energy during cooking process
• Newer electric systems contain new induction cookers instead of coils
• New cookers apply electromagnetic to eddy currents on the metallic bottoms to transfer heat directly, without losing heat
• Induction cookers implement ceramic insulators, and can be observed to maintain 80% efficiency versus 43% in gas systems.

Transformers

• Transformers can manipulate AC voltage whether increasing or decreasing it.
• Found in several electronic and power systems such as televisions, monitors, and electronic keyboards.
• Each are composed through two insulated wires or known as "primary coils" and "secondary coils"
• Wires are linked through electromagnetically attracted components that contain soft Iron. Primary induction to secondary coils allows for AC voltage to terminals at same frequency applied to primary volts

Transformer Voltage

• Differences within original or primary voltage and new secondary voltages depend on design
• Increased number of secondary coils against primary results in great changes to flux
• Faraday analysis shows Secondary equation is as follows: Vs=ns(ΔΦ/Δt)
• Alternately, equation on Input Primary equation is: Vp=np(ΔΦ/Δt)
• Combining both equations shows the transformer equation: Vp/Vs=nP/nS
• Step up transformer show secondary voltage is greater than input, vice-versa in Step down transformer.

Conservation of Energy

• Energy is neither created nor destroyed and transformed from alternative forms
• Electricity supplied relies directly from primary and secondary power transfer from said coils
• If 100J applied to primary, approximately 100j can be applied from secondary
• Energy is lost by transforming into heat through eddy currents, useable energy decreases.
• The rate of energy is expressed as power: P=VI
• Conservation of energy shows primary power equals secondary: Ps=Ps
• Substituting variables shows VpIp = VsIs, alongside equation above combines with the transformer in additional equations: I(s)/I(p)=nP/nS

Common Limitations

• While power of output has potential to equal rate of input
• Secondary voltage and currents show some limited potential
• Incomplete linkages- Magnetic field generated from primary passes entirely through secondary
• Resistive Heat- thin copper passes currents in the primary and secondary
• eddy currents in iron core- changing magnetic fields generates force around the electrons

Eddy Current Reduction

• Insulator layers of iron cores reduce eddy currents using laminated metals and materials known as "ferrites"
• Ferrites consist of unique compounds combining metal oxides and iron
• Ferrites are not electrical conductors, although they pass and transmit magnetic fluxes.
• In high voltage transmissions, power stations exist with long distances from cities due to line loss.
• Over large length transmission, losses present high voltages despite great resistance.
• In metallic conductors as transmission, resistance proportional to resistivity, length, inversed through sectional Area.

Transmission Lines

• Increased voltage reduces currents , while decreased currents can cause fourfold power loss. Reduction allows hundred-fold power loss
• Formula calculates losses due to transmissions losses.
• Ploss=I^2 *R
• Power is a factor of current and resistance. P=VI