Lecture Notes

Acknowledgment of Evaluations

• Thanks for student evaluations; they were helpful.
• Emailed about fifty students; had interesting exchanges.
• Mixed feelings about recitation instructors:
  • Many are happy.
  • Some are moderately happy.
  • Some are very unhappy.
    • Students should switch if very unhappy.

Course Structure

• Thirteen recitation instructors available; easy to switch.
• Some students desire more problem-solving in lectures, but lectures focus on concepts.
• Lectures include:
  • Conceptual discussions
  • Numerical examples to support concepts
  • Demonstrations to illustrate concepts

Exam Feedback

• Mixed feedback on exam difficulty:
  • Some found it too easy.
  • Some found it too hard.
  • Complexity of problems vs. ease of exam construction noted.
• Emphasis on understanding physics, not just math skills.
  • Homework solutions available online to aid understanding.

Homework Assignments

• Average score of 3.8; ideal is 4.0.
• Homework considered too long by many; will reduce assignments by 25%.
• Assignment number five has two problems removed.

Current Lecture Topic: Electromagnetic Induction

• Conceptually challenging material.
• Historical context:
  • Oersted (1819): Steady current produces magnetic field.
  • Faraday: Proposed changing magnetic field induces current (this was confirmed).

Electromagnetic Induction

• Experiment with solenoid and loop:
  • Current flows when switch is closed/open; no current with steady magnetic field.
  • Key finding: Changing magnetic field (not steady) induces current.
• Lenz's Law:
  • Induced current flows in a direction to oppose the change in magnetic field.
  • Useful for determining current direction in circuits.

Demonstration

• Demonstrated induced current using a bar magnet and a loop.
  • Current flowing based on the direction of magnet movement.
  • Fast movement = stronger current; slow movement = minimal current.

Faraday's Law

• Induced EMF (Electromotive Force) = induced current × resistance.
• Faraday's findings:
  • EMF generated in a wire is proportional to the change in magnetic flux.
  • Magnetic flux defined as the integral of the magnetic field over a surface.

Key Equations

• Faraday’s Law:
  • Closed loop integral of E dot dl = -d(Flux)/dt
• The surface area is crucial; changing magnetic flux generates EMF.

Non-Conservative Fields

• Discussion of non-conservative electric fields in circuits.
• Kirchhoff's Rule holds only when electric fields are conservative.
• Non-conservative fields imply the integral of E dot dl depends on the path taken.

Final Demonstration

• Replaced battery with a solenoid to show induced current due to changing magnetic field.
• Measured voltage drop and current flow under changing magnetic conditions.
• Discussion of results obtained with voltmeters showing different potentials based on path taken.

Conclusion

• Significant differences in measurements are indicative of non-conservative fields.
• Faraday's law is fundamental; Kirchhoff’s is a special case.
• Encouragement to reflect on understanding non-intuitive aspects of physics.