Faraday's Law of Electromagnetic Induction and Lenz's Law

Basics of Electromagnetic Induction

• Moving a magnet into a coil can induce a current.
  • Current flows counterclockwise when magnet moves in.
  • Current flows clockwise when magnet moves out.
• Faster movement of the magnet results in a larger induced current.
• Induced current can also be generated by changing the area or angle of the coil.

Magnetic Flux

• Defined as the product of magnetic field (B), area (A), and cosine of the angle (θ).
• Measured in Webers (Wb).
• Induced EMF is proportional to the rate of change of magnetic flux.

Faraday’s Law

• Induced EMF (ε) is equal to the negative rate of change of the magnetic flux through a circuit.
• Formula: ε = -N (ΔΦ/Δt), where N is the number of loops.

Right-Hand Rule

• Used to determine the direction of the magnetic field around a current-carrying wire.
• Thumb points in the direction of the current, and fingers curl in the direction of the magnetic field.

Lenz's Law

• Induced EMF generates a current whose magnetic field opposes the original change in flux.
• Ensures that the system resists change in magnetic flux.

Example Applications

• Direction of Induced Current:
  • Induced current direction in response to changing magnetic flux for various arrangements.
• Rectangular Coil in Magnetic Field:
  • Increasing area increases flux, inducing a current to oppose this.
• Induced EMF for Various Configurations:
  • Calculations for induced EMF in different scenarios, using varying speeds, areas, and angles.

Formulas and Key Equations

• Magnetic Flux: Φ = B * A * cos(θ)
• Induced EMF: ε = -N (dΦ/dt)
• Magnetic Force on a Wire: F = I * L * B * sin(θ)
• Induced EMF in Moving Conductor: ε = B * L * v*

Examples and Problems

• Calculation of induced EMF and current using Faraday's law in different scenarios.
• Determining the direction of current using Lenz’s law.

Transformers

• Step-Up and Step-Down Transformers:
  • Voltage and current transformations through primary and secondary coils.
  • Power conservation in ideal transformers.
• Key Equations:
  • Vs/Vp = Ns/Np for voltage transformation.
  • Ip/Is = Ns/Np for current transformation.

Inductors and Inductance

• Inductance: Measured in Henrys (H), depends on coil parameters.
• Inductor Energy Storage: U = 1/2 L * I^2
• Energy Density: u = B^2 / (2 * μ₀)

Practical Applications and Calculations

• Examples demonstrating the calculation of induced EMF, inductance, and power in circuits.
• Use of formulas to solve problems related to magnetic fields, current, and transformers.