Electromagnetic InductionMind Map

Magnetic flux measures how much magnetic field passes through a surface. For a uniform magnetic field through a plane surface, flux is ΦB = BA cosθ, where θ is the angle between magnetic field B and area vector A. The area vector is perpendicular to the surface, so a surface perpendicular to the field has maximum flux, while a surface parallel to the field has zero flux. Flux can be changed by changing magnetic field strength, area of the loop or orientation of the loop. This makes flux the central quantity in electromagnetic induction, because Faraday’s law says induced emf appears when magnetic flux linked with a circuit changes with time.

Faraday’s law is the central law of electromagnetic induction. Faraday’s first law states that whenever magnetic flux linked with a circuit changes, an emf is induced in the circuit; if the circuit is closed, an induced current flows. Faraday’s second law gives the magnitude of induced emf: it equals the rate of change of magnetic flux linkage. For a coil of N turns, ε = -N dΦB/dt. The negative sign represents Lenz’s law, which gives direction. Induced emf can be produced by moving a magnet near a coil, changing current in a nearby coil, rotating a loop in a magnetic field or changing the area of a circuit. Many devices like generators, transformers and induction cookers are based on this law.

Lenz’s law gives the direction of induced emf and current. It states that the induced current flows in such a direction that its magnetic effect opposes the change in magnetic flux that produced it. The law does not say induced current always opposes the magnetic field; it opposes the change in flux. If flux into a coil increases, induced current produces a field outward. If flux into a coil decreases, induced current produces a field inward to support it. Lenz’s law follows conservation of energy because if induced current helped the change, energy would be created without work. Fleming’s right-hand rule is useful for direction of induced current in a moving conductor. Eddy currents are circulating induced currents in bulk conductors.

Motional emf is the emf induced across a conductor moving through a magnetic field. When a conducting rod moves with velocity v perpendicular to a magnetic field B, free charges inside it experience magnetic force q(v × B). This separates charges at the ends of the rod, creating an electric field and potential difference. For a rod of length l moving perpendicular to B and its length, induced emf is ε = Blv. In sliding rod problems, a rod moving on conducting rails changes the area of the loop, so magnetic flux changes and current flows if the circuit is closed. Mechanical work is required to keep the rod moving because induced current experiences a magnetic force opposing motion, consistent with Lenz’s law.

Self inductance is the property of a coil by which it opposes change in current through itself. When current changes, magnetic flux linked with the same coil changes and an induced emf appears: ε = -L dI/dt. The coefficient of self induction L depends on coil geometry, number of turns, core material and length. Energy is stored in the magnetic field of an inductor and equals U = 1/2 LI². Mutual inductance occurs when changing current in one coil induces emf in a nearby coil: ε2 = -M dI1/dt. This is the basic principle of transformers, where changing AC current in the primary coil induces emf in the secondary coil through changing magnetic flux.

An AC generator converts mechanical energy into electrical energy using electromagnetic induction. It works on the principle that when a coil rotates in a magnetic field, the magnetic flux linked with it changes continuously, inducing emf. The main parts are a rotating armature coil, strong magnetic field, slip rings and brushes. Slip rings rotate with the coil and maintain electrical contact with external circuit through brushes, allowing alternating output. If the coil has N turns and area A rotating with angular speed ω in field B, flux is Φ = NBA cosωt and induced emf is ε = NBAω sinωt. The output alternates direction every half rotation. A DC generator uses split rings instead of slip rings to obtain unidirectional output.