Notes from Toppers

Magnetic Fields and EM Waves

Magnetic Fields

  • Biot-Savart Law:
  • Mathematical expression: dB=μ0idl×r^4πr2
  • Ampère’s Law:
  • Relationship between magnetic field and current: Bdl=μ0Ienc
  • Applications in finding the magnetic field created by simple current-carrying conductors like straight wires, solenoids, and toroids.

Electromagnetic Induction

  • Faraday’s Law:
  • Induced EMF: E=dΦBdt
  • Lenz’s Law:
  • Determining the direction of induced EMF and current.
  • Applications: Generators, transformers, and motors.
  • Motional EMF: E=vBLsinθ

EM Waves

  • Maxwell’s Equations:
  • Four fundamental equations governing electromagnetic phenomena.
  • Wave Equation:
  • Describes the propagation of electromagnetic waves: (2t2v22)E=0
  • Transverse Nature:
  • Oscillations are perpendicular to the direction of propagation.
  • Plane EM Waves:
  • Mathematical description: E=E0^cos(kzωt)
  • Energy Density and Power:
  • Poynting vector: S=1μ0E×B

Additional Concepts:

  • Displacement Current:
  • Maxwell’s addition to Ampere’s law: Id=ϵ0dΦEdt
  • Boundary Conditions:
  • Relations for EM fields at interfaces between different media.
  • Reflection and Refraction:
  • Behavior of EM waves at dielectric interfaces.
  • Polarization:
  • Linear, circular, and elliptical polarization states.

References

  • NCERT Physics, Class 11: Chapter 4 (Motion in a Plane), Chapter 5 (Laws of Motion), Chapter 6 (Work, Energy, and Power).
  • NCERT Physics, Class 12: Chapter 6 (Electrostatics), Chapter 7 (Current Electricity), Chapter 8 (Magnetic Effects of Current), Chapter 9 (Electromagnetic Induction).


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