Physics 2 - Electromagnetic Induction Notes

General Concepts of Electromagnetic Induction

  • Electromagnetic Induction:
    • The process of inducing an electric current in a circuit via a changing magnetic field.

Key Terms

  • Electromotive Force (EMF):
    • Definition: The voltage generated by a battery or by a magnetic force according to Faraday’s Law.
    • Measurement: Measured in volts, it is not a force.
  • Solenoid:
    • A coil of wire that behaves like a magnet when an electric current flows through it.
  • Flux:
    • The rate of energy transfer through a given surface.

Magnetic Flux

  • Magnetic Flux (Φ):
    • Indicates the amount of magnetic field passing through a surface.
    • Proportional to the number of magnetic field lines through the given surface.
  • Formula:
    • [ \Phi_B = B A \cos(\theta) ]
    • [ \Phi ]: Magnetic flux
    • [ B ]: Magnetic field strength
    • [ A ]: Area of surface through which flux is measured
    • [ \theta ]: Angle between magnetic field lines and the normal line to the surface.

Faraday's Law of Induction

  • Definition:
    • Predicts how a magnetic field interacts with an electric circuit to generate an EMF.
  • Historical Context:
    • Proposed by Michael Faraday in 1831 based on experimental observations.
  • Induction Process:
    • Stationary Magnet: No current induced in coil.
    • Moving Magnet: Induces current when moved toward or away from the coil.
    • Current-Carrying Coil: Induced current occurs when this coil moves relative to the stationary coil.

Factors Affecting Induced Voltage

  • Number of Loops: Increasing the number of loops strengthens induced voltage.
  • Rate of Change of Magnetic Field: Faster changes induce higher voltages.

Mathematical Formulation of Faraday's Law

  • Formula:
    • [ \text{EM} = - N \frac{\Delta \Phi}{\Delta t} ]
    • [ \text{EM} ]: Electromotive force
    • [ N ]: Number of loops in the coil
    • [ \Delta \Phi ]: Change in magnetic flux
    • [ \Delta t ]: Time over which the change occurs.

Example Calculations

  1. Example 1: A circular coil with a radius of 3 cm and 50 loops, magnetic field changes from 0.10 T to 0.35 T in 2ms:
    • Calculate change in magnetic flux.
    • Average EMF: [ \text{EM} = 17.68 V ]
  2. Example 2: Circular coil with a radius of 6 cm, 70 loops, magnetic field changes from 0.20 T to 0.65 T in 5ms:
    • Average EMF: [ \text{EM} = 71.4 V ]
  3. Example 3: Circular coil with a radius of 7 cm, 50 loops, magnetic field changes from 0.10 T to 0.75 T in 3 ms:
    • Average EMF: [ \text{EM} = 166.67 V ]

Lenz's Law

  • Statement:
    • An induced EMF will always be in a direction that opposes the change in magnetic flux that produces it.

Special Cases and System Components

  • Direct Current (DC):
    • Flows in one direction, used in battery-powered devices.
  • Alternating Current (AC):
    • Flow direction alternates with the EMF; used in electric motors and appliances.
  • LC Circuits:
    • Combinations of inductors and capacitors, allowing energy oscillation between the two components, producing continuous cycles of energy transfer.