Electrodynamics: Lecture 1

Introduction

• Channel: Prince Chadda
• Topic: Electrodynamics
• Objective: Discussion on important topics using mathematics in electrodynamics

Key Points

Coordinate System

• Three Types: Cartesian, Spherical, Cylindrical
• Why Useful: They're used in various calculations and theorems in electrodynamics

Cartesian Coordinate System

• Usage: X, Y, Z axes
• Length Element: DLx, DLy, DLz
• Surface Element: Dsx = DyDz, Dsy = DxDz, Dsz = DxDy
• Volume Element: DV = DxDyDz
• Distance Formula:

Spherical Coordinate System

• Coordinates: r, θ (theta), φ (phi)
• Length Element:
  • DLr = Dr
  • DLθ = rDθ
  • DLφ = rsinθDφ
• Surface Element:
  • For r: r²sinθDθDφ
  • For θ: rDrDφ
  • For φ: rDθDr
• Volume Element: r²sinθDrDθDφ
• Limits:
  • r: 0 to ∞
  • θ: 0 to π
  • φ: 0 to 2π

Cylindrical Coordinate System

• Coordinates: ρ (rho), φ (phi), z
• Length Element:
  • DLρ = Dρ
  • DLφ = ρDφ
  • DLz = Dz
• Surface Element:
  • For ρ: ρDφDz
  • For φ: DρDz
  • For z: ρDρDφ
• Volume Element: ρDρDφDz
• Limits:
  • ρ: 0 to ∞
  • φ: 0 to 2π
  • z: -∞ to ∞

Important Formulas and Theorems

• Next Lecture: Gradient, Divergence, Curl, and the three theorems
• Properties: Calculations involving direction and the position of points

Conclusion

• Heat Issue: Unable to use the cooler, so recordings will be done in the mornings
• Next Lecture Plan: Focus on theorems and properties