Summary

• Separation of variables
• Multipole expansion

Chapter 3 overview


• Separation of variables in Cartesian coordinates
• Fourier's trick
• hyperbolic functions



• Separation of variables in spherical coordinates
• Legendre polynomials
• "pattern matching"



• Multipole expansion
• approximate potentials
• dipole potential and field



• Examples
• Griffiths 3.47
• KLM: V(R,θ) = V₀sin²θ cos²θ
• Griffiths 3.40