Lecture Notes on Faraday's Law and Lenz's Law

Faraday's Law of Electromagnetic Induction

• Induction of Current:
  • Moving a magnet into a coil induces a current in the coil.
  • Direction depends on the motion:
    • Into coil: current counterclockwise.
    • Away from coil: current clockwise.
• Dependence on Speed:
  • Faster movement of the magnet induces a larger current.
  • No movement results in no current.
• Other Methods of Inducing Current:
  • Changing the area of the coil (e.g., stretching or bending).
  • Changing the angle of the coil relative to the magnetic field.

Magnetic Flux

• Formula: Magnetic Flux = B * A * cos(θ)
  • B = Magnetic field in Tesla
  • A = Area in square meters
  • θ = Angle between magnetic field and normal to the surface
• Units: Weber (Wb) = Tesla * square meter
• Induced EMF: Proportional to the rate of change of magnetic flux.*

Cases of Magnetic Field Orientation

• Parallel to normal line: Maximum flux
• Perpendicular to normal line: Zero flux

Lenz's Law

• Principle: Induced EMF generates a current whose magnetic field opposes the change in flux.
• Application: If the external magnetic field is increasing, the induced field will work against it, and vice versa.

Right-Hand Rule

• Magnetic Field Direction:
  • Thumb points in direction of current.
  • Fingers curl in the direction of the magnetic field.

Examples

• Rectangular Conductor in Magnetic Field:
  • Current direction depends on whether the conductor is moving into or away from the magnetic field.
  • Lenz’s Law helps determine this by opposing changes in flux.

Induced EMF and Current Calculations

• Faraday's Law Equation:
  • Induced EMF = -N * Δ(Flux)/Δt
  • N = Number of turns/coils
• Voltage and Current Relationship:
  • EMF can be treated like voltage: V = IR
• Examples of Calculations:
  • Change in magnetic flux and induced EMF calculations
  • Work through example problems with given turns, magnetic fields, and resistances.*

Transformers

• Components:
  • Primary and secondary coils around an iron core.
  • Step-up (increases voltage) or step-down (decreases voltage) based on coils ratio.
• Formula Relationships:
  • Ns/Np = Vs/Vp = Ip/Is
  • Power conservation: Vs * Is = Vp * Ip (ideal transformers)
• Examples of Transformer Calculations:
  • Calculating secondary voltage, current, and turns.

Additional Topics

• AC Generators
  • Induced EMF = N * B * A * ω * sin(ωt)
  • Angular velocity ω = 2πf
• Inductance and Solenoids
  • Inductance L = μ₀ * N² * A / L
  • Induced EMF = -L * ΔI/Δt
• Energy in Inductors
  • Potential energy stored: 1/2 * L * I²
  • Energy density: U = B² / (2μ₀)*

Key Terms

• Weber (Wb): Unit of magnetic flux.
• Tesla (T): Unit of magnetic field strength.
• Henry (H): Unit of inductance.

These notes summarize the key concepts from the lecture on Faraday's Law of Electromagnetic Induction and Lenz's Law, including their applications and relevant calculations.