Magnetic coupling and mutual inductance are key concepts in understanding how energy transfers between circuits. They explain how transformers work and why nearby wires can interfere with each other's signals.

This topic builds on basic magnetic field principles to show how changing currents create magnetic fields that induce voltages in nearby conductors. It's crucial for grasping how energy moves in complex electrical systems.

Magnetic Coupling

Magnetic Flux and Mutual Inductance

• Magnetic flux measures the total magnetic field passing through a given area
• Flux density represents the strength of the magnetic field at a specific point
• Mutual inductance occurs when the changing magnetic field of one coil induces a voltage in another nearby coil
• Mutual inductance value depends on coil geometry, number of turns, and core material
• Measured in henries (H), mutual inductance quantifies the strength of magnetic coupling between two coils

Coupling Coefficient and Flux Linkage

• Coupling coefficient (k) indicates the degree of magnetic coupling between two coils
• k ranges from 0 (no coupling) to 1 (perfect coupling), with typical values between 0.1 and 0.9
• Flux linkage represents the total magnetic flux linking two coils
• Calculated by multiplying the magnetic flux by the number of turns in the coil
• Higher flux linkage results in stronger magnetic coupling and increased mutual inductance

Electromagnetic Induction

Faraday's Law of Induction

• Faraday's law states that a changing magnetic field induces an electromotive force (EMF) in a conductor
• Induced EMF is proportional to the rate of change of magnetic flux through the conductor
• EMF magnitude depends on the number of turns in the coil and the rate of flux change
• Applications include transformers, generators, and induction cooktops

Lenz's Law and Magnetic Field Interactions

• Lenz's law describes the direction of induced current in a conductor
• Induced current creates a magnetic field that opposes the change in the original magnetic field
• Explains the back EMF in motors and generators
• Magnetic field strength decreases with distance from the source (inverse square law)
• Magnetic field lines form closed loops, never intersecting each other

Inductance

Self-Inductance and Energy Storage

• Self-inductance occurs when a changing current in a coil induces a voltage in the same coil
• Measured in henries (H), self-inductance depends on coil geometry and core material
• Energy stored in an inductor is proportional to the square of the current flowing through it
• Self-inductance causes a delay in current changes, known as inductive reactance
• Applications include filters, chokes, and energy storage in power supplies

Dot Convention and Mutual Inductance Polarity

• Dot convention provides a visual representation of coil winding direction and mutual inductance polarity
• Dots placed on coil ends indicate the direction of induced voltage relative to current flow
• Current entering a dot on one coil induces voltage with the dot positive on the coupled coil
• Useful for determining phase relationships in transformer windings and coupled circuits
• Helps in analyzing and designing circuits with multiple inductors or transformers