2) The next tutorial is scheduled for Tuesday, Oct 30, 2012 at 10:30 in A5:1041 (Seminar room of the Cops group)

The students' overall performance will be graded on a 7 point scale (A - E, Fx,F). The grading criteria is available here .

Some extra problems and solutions

• Definitions and meanings of Gradient, Divergence and Curl
• The notions of directional derivative and path-independence
• Divergence theorem
• Stokes's threorm
• Solutions of curl A = 0 and div A = 0
• Examples: gradient and Laplacian of 1/r.

• 1.1 Coulomb's Law
• 1.2 Electric Field
• 1.3 Gauss's Law
• 1.4 Differential Form of Gauss's Law
• 1.5 Another Equation of Electrostatics and the Scalar Potential
• 1.6 Surface Distribution of Charges and Discontinuities in the Electric Field (Excluding the part on the Dipole Layer).
• 1.7 Poisson and Laplace Equations (For the Laplacian of 1/r, an alternative derivation was presented in the class )
• 1.8 Green's Theorem
• 1.9 Uniqueness of the Solution with Dirichlet or Neumann Boundary Conditions
• 1.10 Formal Solution of Electrostatic Boundary-Value Problem with Green Function
• 1.11 Electrostatic Potential Energy and Energy Density (Excluding the part on Capacitance ). (The derivation for the contiuous case given in the class differs from that in the Textbook)

• 2.1 Method of Images
• 2.2 Point Charge in the Presence of a Grounded Conducting Sphere
• 2.3 Point Charge in the Presence of a Charged, Insulated, Conducting Sphere
• 2.4 Point Charge Near a Conducting Sphere at Fixed Potential
• 2.6 Green Function for the Sphere, General Solution for the Potential
• 2.8 Orthogonal Functions and Expansions
• 2.9 Separation of Variables, Laplace Equation in Rectangular Coordinates

• 3.1 Laplace Equation in Spherical Coordinates
• 3.2 Legendre Equation and Legendre Polynomials (Rodrigue's formula, Recurrence relations, orthogonality - no derivations)
• 3.3 Boundary-Value Problem with Azimuthal Symmetry
• 3.5 Associated Legendre Functions and the Spherical Harmonics
• 3.6 Addition Theorem for Spherical Harmonics (no derivation)
• 3.9 Expansion of Green Functions in Spherical Coordinates

• 4.1 Multipole Expansion
• 4.2 Multipole Expansion of the Energy of a Charge Distribution in an External Field
• 4.3 Elementary Treatment of Electrostatics with Ponderable Media
• 4.4 Boundary-Value Problems with Dielectrics (upto equation 4.47)
• 4.7 Electrostatic Energy in Dielectric Media

• 5.1 Introduction and Definitions (more detailed discussion of the continuity equation)
• 5.2 Biot and Savart Law
• 5.3 Differential Equations of Magnetostatics and Ampere's Law
• 5.4 Vector Potential
• 5.6 Magnetic Fields of a Localized Current Distribution, Magnetic Moment
• 5.7 Force and Torque on and Energy of a Localized Current Distribution in an External Magnetic Induction
• 5.8 Macroscopic Equations, Boundary Conditions of B and H
• 5.15 Faraday's Law of Induction
• 5.16 Energy in the Magnetic Field

• 6.1 Maxwell's Displacement Current; Maxwell Equations
• 6.2 Vector and Scalar Potentials
• 6.3 Gauge Transformations, Lorentz Gauge, Coulomb Gauge
• 6.4 Green Functions for the Wave Equation
• 6.5 Retarded Solutions for the Fields: Jefimenko's Generalizations of the Coulom and Biot-Savart Laws
• 6.7 Poynting's Theorem and Conservation of Energy and Momentum for a System of Charged Particles and Electromagnetic Fields
• 6.10 Transformation Properties of Electromagnetic Fields and Sources under Rotations, Spatial Reflections, and Time Reversal

• 9.1 Fields and Radiation of a Localized Oscillating Source
• 9.2 Electric Dipole Fields and Radiation

• Boundary conditions at interfaces between different media (page 16-19 of Jackson)

• (See lecture notes above)