Faraday's Law of Electromagnetic Induction

Introduction

• Focus: Faraday's Law of Electromagnetic Induction
• Example: Iron bar wrapped with coils of wire, voltmeter, second set of coils, battery, and resistor.

Key Concept

• Steady current: No emf or induced current in the second coil.
• Closing the switch: Induced current for a brief period.
• Why?: Change in current relates to Faraday's Law — changing magnetic field induces current.

Faraday's Law Formula

• Induced Emf (𝓔) = -N * (ΔΦ / Δt)
  • N: Number of turns
  • Φ: Magnetic flux
  • ΔΦ: Change in flux
  • Δt: Change in time
• Faster flux change = Greater induced emf.
• Magnetic Flux (Φ) = Magnetic Field (B) * Area (A) * cos(θ)
  • θ: Angle between normal line and magnetic field

Methods to Induce Emf

1. Change Magnetic Field

   • Move magnet in or out of coil
   • Increased or decreased magnetic field = Change in flux = Induced emf

2. Change Area of Coil

   • Increase/decrease coil's area
   • Change in area = Change in flux = Induced emf

3. Change Angle Between Magnetic Field and Normal Line

   • Rotate coil to change angle
   • Change in angle (θ) = Change in flux = Induced emf

Example Problem

Setup: Square Coil with 50 Loops

• Magnetic field perpendicular to face of coil
• Magnetic field change: -3 T to 5 T
• Coil connected to resistor

Calculations

• Induced Emf:
  • Formula: -N * (Δ(BA cos(θ)) / Δt)
  • Change in B: 5 T - (-3 T) = 8 T
  • Area (A): 0.2 m * 0.2 m = 0.04 m²
  • θ: 0 degrees (cos(0) = 1)
  • Δt: 0.1 s
  • Calculation: -50 * 8 T * 0.04 m² * 1 / 0.1 s = -160V
• Current Calculation:
  • I = 𝓔 / R = 160V / 20Ω = 8 A
• Power Dissipated:
  • P = I² * R = 8² * 20Ω = 1280 Watts

Conclusion

• Importance of number of loops: More loops = Greater induced emf.
• Practical implications: More loops lead to higher power generation.