Maxwell's Equations

🔖 Topics

• Displacement current
• Maxwell's equations
• Electromagnetic waves

🎯 Objectives

• Explain Maxwell's contributions to electromagnetic theory
• Explain why displacement current is a necessary addition to Ampere's law
• Compile Maxwell's four equations
• Describe some of the uses of Maxwell's equations in electromagnetic theory

📋 Sequence

• Maxwell’s add-on to Ampere’s law
  • Consider a capacitor in a circuit with a long wire
  • Draw an Amperian surface passing between the plates of the capacitor
  • Magnetic fields depend on current AND changing electric field
• Maxwell’s equations
  • Gauss’s law for electricity - electric field lines emanate / terminate on electric charges
  • Gauss’s law for magnetism - magnetic field lines are closed loops (i.e. there are no magnetic charges)
  • Faraday’s law of induction - changing magnetic fields produce electric fields
  • Ampere-Maxwell law - changing electric fields and currents produce magnetic fields

🖥️ Animations, Simulations, Activities

• Displacement current demo - https://www.youtube.com/watch?v=EqufEpWaKXw

📝 Practice Problems

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✅ Partial Solutions

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📘 Connected Resources

• Caltech’s Feynman Lecture Hall. Demo 12501: Displacement Current. April 2020.
• Giambattista, Alan, et al. College Physics With an Integrated Approach to Forces and Kinematics. 5th ed., McGraw-Hill Education, 2020.