Electromagnetic Induction Lesson 30 by Owen Borville 1.1.2026
Electromagnetic induction is the process where a changing magnetic field creates an electric current (or voltage) in a conductor, like a wire coil, as discovered by Michael Faraday. Electromagnetic induction occurs when a conductor moves through a magnetic field, or the magnetic field changes around a stationary conductor converting magnetic energy into electric energy and powering devices like generators, transformers, and wireless chargers.
The key quantity in electromagnetic induction is magnetic flux Φ = BA cos θ, where B is the magnetic field strength of a uniform magnetic field over an enclosed area A at an angle θ with the perpendicular to the area. Magnetic flux through an enclosed area is the amount of field lines cutting through a surface area A defined by the unit area vector. Units of magnetic flux are webers, 1 Wb = T*m^2. Any change in magnetic flux induces an emf, which is the process defined to be electromagnetic induction.
Magnetic flux can also be described mathematically when the magnetic field is not uniform as the integration of magnetic field B by summing the infinitely small area elements dA over the entire surface S by ( ∫ s B dA).
The induced emf in a closed loop due to a change in magnetic flux through the loop is described by Faraday's law. If there is not change in magnetic flux, no induced emf is created.
Faraday's law of induction states that the emf induced by a change in magnetic flux is emf = -N ΔΦ/Δt when flux changes by ΔΦ in a time Δt (or -NdΦm/dt). If emf is induced in a coil, N is its number of turns. The minus sign means that the emf creates a current I and magnetic field B that oppose the change in flux ΔΦ according to Lenz's law. No change in magnetic flux results in no induced emf created. Lenz's law is used to determine the directions of induced magnetic fields, currents, and emfs. The direction of an induced emf always opposes the change in magnetic flux that causes the emf, according to Lenz's law.
A changing magnetic flux induces an electric field and both the changing magnetic flux and the induced electric field are related to the induced emf from Faraday's law.
Motional Emf is induced by motion in a wire relative to a magnetic field B: emf (ε) = Blv, where B, l, and v are perpendicular, l is the length of the object moving at constant speed v relative to the field. An induced emf from Faraday's law is created from a motional emf that opposes the change in flux. Using mathematical integration, motional emf around a circuit is ∫E*dl = - dΦm/dt
Eddy currents are current loops or spiral shaped currents induced in moving electric conductors when they are placed inside a changing magnetic field and they can create significant drag, called magnetic damping. Applications of eddy current manipulation are in metal detectors, braking in trains or roller coasters, and induction cooktops.
Electric generators rotate on a coil in a magnetic field, inducing an emf given as a function of time: emf = NABω sin ωt where A is the area of an N-turn coil rotated at a constant angular velocity ω in a uniform magnetic field B. The peak emf0 of a generator is emf0 = NABω. Any rotating coil produces an induced emf.
Back emf is any rotating coil that has an induced emf in motors because it opposes the emf input to the motor.
Applications of electromagnetic induction include hard drives in computers to read and write information, in addition to graphics tablets, wireless charging phones, induction cooktops, electric and hybrid vehicles, magnetic flow meters, and in transcranial magnetic stimulation.
Transformers are electrical devices that use induction to transform voltages between circuits from one value to another using electromagnetic induction to increase or decrease voltage levels without changing frequency. For a transformer, the voltages across the primary and secondary coils are related by: Vs/Vp = Ns/Np where Vp and Vs are the voltages across primary and secondary coils having Np and Ns turns. The currents Ip and Is in the primary and secondary coils are related by: Is/Ip = Np/Ns. A step-up transformer increases voltage and decreases current, whereas a step-down transformer decreases voltage and increases current.
Electrical safety systems and devices are employed to prevent thermal and shock hazards. Circuit breakers and fuses interrupt excessing currents to prevent thermal hazards. The three-wire system guards against thermal and shock hazards, utilizing live/hot, neutral, and earth/ground wires, and grounding the neutral wire and case of the appliance. A ground fault interrupter (GFI) prevents shock by detecting the loss of current to unintentional paths. An isolation transformer insulates this device being powered from the original source, also to prevent shock. Many of these devices use induction to perform their basic function.
Electromagnetic induction is the process where a changing magnetic field creates an electric current (or voltage) in a conductor, like a wire coil, as discovered by Michael Faraday. Electromagnetic induction occurs when a conductor moves through a magnetic field, or the magnetic field changes around a stationary conductor converting magnetic energy into electric energy and powering devices like generators, transformers, and wireless chargers.
The key quantity in electromagnetic induction is magnetic flux Φ = BA cos θ, where B is the magnetic field strength of a uniform magnetic field over an enclosed area A at an angle θ with the perpendicular to the area. Magnetic flux through an enclosed area is the amount of field lines cutting through a surface area A defined by the unit area vector. Units of magnetic flux are webers, 1 Wb = T*m^2. Any change in magnetic flux induces an emf, which is the process defined to be electromagnetic induction.
Magnetic flux can also be described mathematically when the magnetic field is not uniform as the integration of magnetic field B by summing the infinitely small area elements dA over the entire surface S by ( ∫ s B dA).
The induced emf in a closed loop due to a change in magnetic flux through the loop is described by Faraday's law. If there is not change in magnetic flux, no induced emf is created.
Faraday's law of induction states that the emf induced by a change in magnetic flux is emf = -N ΔΦ/Δt when flux changes by ΔΦ in a time Δt (or -NdΦm/dt). If emf is induced in a coil, N is its number of turns. The minus sign means that the emf creates a current I and magnetic field B that oppose the change in flux ΔΦ according to Lenz's law. No change in magnetic flux results in no induced emf created. Lenz's law is used to determine the directions of induced magnetic fields, currents, and emfs. The direction of an induced emf always opposes the change in magnetic flux that causes the emf, according to Lenz's law.
A changing magnetic flux induces an electric field and both the changing magnetic flux and the induced electric field are related to the induced emf from Faraday's law.
Motional Emf is induced by motion in a wire relative to a magnetic field B: emf (ε) = Blv, where B, l, and v are perpendicular, l is the length of the object moving at constant speed v relative to the field. An induced emf from Faraday's law is created from a motional emf that opposes the change in flux. Using mathematical integration, motional emf around a circuit is ∫E*dl = - dΦm/dt
Eddy currents are current loops or spiral shaped currents induced in moving electric conductors when they are placed inside a changing magnetic field and they can create significant drag, called magnetic damping. Applications of eddy current manipulation are in metal detectors, braking in trains or roller coasters, and induction cooktops.
Electric generators rotate on a coil in a magnetic field, inducing an emf given as a function of time: emf = NABω sin ωt where A is the area of an N-turn coil rotated at a constant angular velocity ω in a uniform magnetic field B. The peak emf0 of a generator is emf0 = NABω. Any rotating coil produces an induced emf.
Back emf is any rotating coil that has an induced emf in motors because it opposes the emf input to the motor.
Applications of electromagnetic induction include hard drives in computers to read and write information, in addition to graphics tablets, wireless charging phones, induction cooktops, electric and hybrid vehicles, magnetic flow meters, and in transcranial magnetic stimulation.
Transformers are electrical devices that use induction to transform voltages between circuits from one value to another using electromagnetic induction to increase or decrease voltage levels without changing frequency. For a transformer, the voltages across the primary and secondary coils are related by: Vs/Vp = Ns/Np where Vp and Vs are the voltages across primary and secondary coils having Np and Ns turns. The currents Ip and Is in the primary and secondary coils are related by: Is/Ip = Np/Ns. A step-up transformer increases voltage and decreases current, whereas a step-down transformer decreases voltage and increases current.
Electrical safety systems and devices are employed to prevent thermal and shock hazards. Circuit breakers and fuses interrupt excessing currents to prevent thermal hazards. The three-wire system guards against thermal and shock hazards, utilizing live/hot, neutral, and earth/ground wires, and grounding the neutral wire and case of the appliance. A ground fault interrupter (GFI) prevents shock by detecting the loss of current to unintentional paths. An isolation transformer insulates this device being powered from the original source, also to prevent shock. Many of these devices use induction to perform their basic function.