Electromagnetic Induction Study Notes

Department of Physics and Astronomy

Chapter 29: Electromagnetic Induction - Overview

In this chapter, we explore the principles of electromagnetic induction, which play a crucial role in the generation of electric power. The grid systems depend on generators that convert mechanical energy into electrical energy, illustrating the application of these principles.

29.1 Faraday's Experiments

  • Key Figures: Michael Faraday, a British chemist and physicist, conducted foundational experiments during the 1830s, which were parallel to the work of Joseph Henry in the U.S.

    • Unit of capacitance: Farad (F)

    • Inductance: Henry (H)

    • Their experiment included using a wire loop connected to an ammeter with a bar magnet some distance from the loop, with its north pole pointing towards the loop.

      • While the magnet is stationary, no current flows in the loop

      • If the magnet is moved toward the loop, a counterclockwise current flows in the loop as indicated by the positive current in the ammeter

      • If the magnet is reversed so the south pole points toward the loop and is moved towards the loop, current flows in the loop in the opposite direction as indicated by the negative current in the ammeter

      • If the north pole of the magnet points toward the loop, and the magnet is then moved away from the loop, a negative clockwise current, as indicated on the ammeter, is induced in the loop

      • If the south pole of the magnet points toward the loop, and the magnet is moved away from the loop, a positive counterclockwise current is induced in the loop, which is reflected by a positive reading on the ammeter.

  • Main Findings: Their experiments demonstrated that a changing magnetic field could induce an electromotive force (emf) or potential difference in a conductor, leading to electric current.

  • Important points:

    • A changing magnetic field generates an electric current and therefore an electric field

    • An electric field is generated only when a magnetic field is in motion or otherwise changes as a function of time

    • If a constant current is flowing through loop 1, no current is induced in loop 2

    • If the current in loop 1 is increased, a current is induced in loop 2 in the opposite direction

      • the induced current is in the opposite direction

      • If current is flowing in loop 1 in the same direction as before and is then decreased, the current induced in loop 2 flows in the same direction as the current in loop 1

  • Experimental Setup:

    • Wire Loop and Ammeter: When a wire loop is connected to an ammeter with a bar magnet nearby:

      • Stationary Magnet: No current flows when the magnet is stationary.

      • Moving Magnet: When the magnet is moved relative to the loop, different scenarios can cause different current flows:

      1. Magnet Approach: Moving the north pole of the magnet towards the loop induces a counterclockwise current (positive reading on ammeter).

      2. Magnet Reversal: If the south pole approaches, the current flows in the opposite direction (negative reading on ammeter).

      3. Magnet Withdrawal: Pulling the magnet away from the loop results in a negative clockwise current for the north pole withdrawal and a positive current for the south pole.

29.2 Faraday's Law of Induction

  • Law Statement: Faraday's Law states that a potential difference is induced in a loop when the number of magnetic field lines through the loop changes over time.

  • Electric Field Generation: The induced potential difference suggests that a changing magnetic field creates an electric field around the loop.

  • Conservative vs Non-Conservative Forces:

    • Electric fields arising from stationary charges exhibit conservative properties, where no work is done moving a charge in a closed loop.

    • Electric fields from changing magnetic fields are not conservative.

    • Conservative forces do no work when they act on an object whose path starts and ends at the same point in space

  • Work Done Equation: The work done on a particle moving in an electric field from a change in potential difference is given by

\text{Work} = \text{Induced Potential Difference} \times \text{Charge}

  • Magnetic Flux: Analogous to electric flux, magnetic flux
    is defined as the product of the magnetic field B and the area A through which it flows, taking angle
    into consideration:

\text{Magnetic Flux} (\text{Φ}) = A \times B \times \text{cos}(\theta)

 Example Cases:

  • If
    is perpendicular (0 degrees),
    \text{Φ} = AB ; if parallel (90 degrees),
    \text{Φ} = 0 .

  • Integral Dependencies:

\text{Φ} = BA

29.5 Induction in a Flat Loop

  • Mathematical Expression: Recasting Faraday’s Law yields:

\Delta V{\text{ind}} = - \frac{d\text{Φ}B}{dt}

29.6 Applications Examples

  • Example Problem: A direct current of
    600 mA generates a magnetic field of 0.025 T in an ideal solenoid, with induced voltage calculated for a circular loop of radius 3.4 cm with N windings.

  • Induced Voltage Calculation: The voltage can be derived from measurements and variations applied over time.

29.7 Induced Electric Field

  • Inductive Reaction: As established from rotation or movement within a magnetic field, induced emf can be derived from the movement of boundaries through a constant magnetic field.

29.8 RL Circuits

  • Circuit Dynamics: Involving a resistor and an inductor, the rate of current change and its effect on self-induction are crucially analyzed through Kirchoff's loop rule and reviewed in chapters involving electromagnetic application in circuitry.

29.9 Energy Stored in Magnetic Fields

  • Energy Concepts: Similar to capacitors storing energy in electric fields, inductors store energy in magnetic fields expressed mathematically in terms of L (inductance) and I (current).

Coordination with external electromagnetic changes yields dynamic energy handling characteristics in circuit design and applications.