Lecture on Faraday's Law of Electromagnetic Induction

Introduction to Faraday's Law

• Concept: Faraday's Law of Electromagnetic Induction explains how a change in magnetic field induces an electromotive force (EMF).
• Basic Setup: An iron bar wrapped with coils of wire connected to a voltmeter and a circuit with a battery and resistor.
• Observation: Steady current induces no EMF, but a changing current does.
• Key Principle: A changing magnetic field induces a current.

Faraday's Law Formula

• Equation: Induced EMF = -n * (ΔΦ/Δt)
  • n = number of loops
  • ΔΦ = change in magnetic flux
  • Δt = change in time
• Magnetic Flux: Φ = B * A * cos(θ)
  • B = magnetic field
  • A = area
  • θ = angle between the field and normal to the coil

Methods to Induce EMF

1. Change Magnetic Field:
   • Moving a magnet into or out of a coil changes the magnetic field, leading to a change in flux and an induced EMF.
   • No induced current if the magnet is stationary.
2. Change Area of Coil:
   • Increasing the area of the coil in a constant magnetic field increases flux, inducing EMF.
3. Change Angle:
   • Rotating the coil changes the angle between the magnetic field and the coil's normal line, altering flux and inducing EMF.

Practice Problem

• Setup: Square coil with 50 loops; magnetic field changes from -3 Tesla to 5 Tesla.
• Induced EMF Calculation:
  • Formula: -n * (ΔB * A * cos(θ)) / Δt
  • Calculation involves the change in magnetic field, area, cosine of angle (0 degrees), and time.
• Result: Induced EMF = -160 volts (ignoring the negative sign for calculations)

Calculation of Current and Power

• Current: I = EMF / Resistance
  • Example: I = 160 volts / 20 ohms = 8 amps
• Power: P = I² * R
  • Example: P = 8² * 20 = 1280 watts

Conclusion

• Impact of Loops: More loops increase induced EMF significantly.
• Practical Application: Changing magnetic fields or flux can generate substantial power, especially with multiple loops.