Faraday's Law of Electromagnetic Induction

Basic Setup

• Components: Iron bar, coils of wire, voltmeter, battery, resistor.
• Observation: No EMF or current induced in the second coil when a steady current flows through the circuit.

Inducing Current

• Switch Activation: Closing the switch causes a momentary induced current in the second coil due to changing current.
• Concept: Change in magnetic field induces EMF in the second coil.

Faraday's Law

• Formula: Induced EMF = -n (ΔΦ/Δt)
  • n: Number of turns in the coil
  • ΔΦ: Change in magnetic flux
  • Δt: Change in time
• Magnetic Flux: Φ = B * A * cos(θ)
  • B: Magnetic field
  • A: Area
  • θ: Angle between magnetic field and normal to the coil

Methods to Induce EMF

1. Change Magnetic Field:

   • Moving a magnet into or out of the coil changes the magnetic field, thus changing the flux.
   • If the magnet is static, no change in flux, hence no induced EMF.

2. Change Area of the Coil:

   • Example: Expanding a circular coil in a constant magnetic field increases flux, inducing EMF.

3. Change Angle:

   • Rotating the coil changes the angle, altering the flux and inducing EMF.
   • Example: Rotating a square coil changes angle from 0 to 70 degrees.

Practice Problem

• Setup:

  • Square coil with 50 loops, magnetic field perpendicular and parallel to the normal.
  • Magnetic field changes from -3 Tesla to 5 Tesla.
  • Coil connected across a 20-ohm resistor.

• Induced EMF Calculation:

  • Formula: Induced EMF = -n (ΔΦ/Δt)
  • Calculation:
    • ΔB = 5 - (-3) = 8
    • Area (A) = 0.2 * 0.2 = 0.04 m²
    • Time (Δt) = 0.1 seconds
    • Result: Induced EMF = -160V

• Current Calculation:

  • Formula: Current (I) = EMF / Resistance
  • Result: I = 160 / 20 = 8 Amps

• Power Calculation:

  • Formula: Power = I² * Resistance
  • Result: Power = 8² * 20 = 1280 Watts*

Key Takeaways

• Changing magnetic field, coil area, or angle can induce EMF.
• Higher number of loops increases the induced EMF dramatically.
• Practical applications involve ensuring sufficient loops to achieve desired EMF levels.