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IPS program: Theoretical Physics 2 (Electrodynamics 1)

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1.1 Orthogonal transformations and tensors

1.2 Vector differential operators

1.3 Integral theorems

1.4 The Dirac delta-function

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I. Electrostatics

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2. Electrostatics in vacuum

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2.1. Coulomb's Law and Gauss's Law

2.2. Another equation of electrostatics and the scalar potential

2.3. Surface distributions of charges and dipoles. Discontinuities
of the electric field and the potential

2.4. Poisson and Laplace equation

2.5. Green's Theorem.
Uniqueness of electrostatic boundary-value problem
and the formal solution
with Green Function

2.6. Electrostatic potential energy and energy density

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3. Boundary value problems in electrostatics

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3.1. Method of images

3.2. Green function for the sphere. General solution for the potential

3.3. Orthogonal functions and expansion

3.4. Laplace equation in rectangular coordinates. Separation of variables

3.5. Laplace equation in polar coordinates

3.6. Laplace equation in spherical coordinates

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4. Multipoles. Electrostatics of macroscopic media

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4.1. Multipole expansion

4.2. Polarisation and electric displacement

4.3. Boundary-value problems with dielectrics

4.4. Electrostatic energy

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II. Magnetostatics

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5. Magnetostatics in vacuum

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5.1. Introduction and definitions

5.2. Biot and Savart Law

5.3. Differential equations of magnetostatics and Ampere's Law

5.4. Vector potential

5.5. Magnetic field of a localized current distribution. Magnetic moment

5.6. Force on a localized current distribution in an external magnetic induction

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6. Magnetostatics of macroscopic magnetic media

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6.1. Macroscopic magnetization and the magnetic field

6.2. Methods of solving boundary-value problems in magnetostatics

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III. Faraday's law and Maxwell equations

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7. Time-dependent magnetic field

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7.1. Faraday's law of induction

7.2. Energy in the magnetic field

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8. Maxwell equations

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8.1. Maxwell's displacement current, continuity equation and Maxwell equations

8.2. Vector and scalar electromagnetic potentials

8.3. Derivation of macroscopic Maxwell equations

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9. Units and dimensions

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9.1. Electromagnetic units and equations

9.2. SI and Gaussian systems of electromagnetic units

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10.1. Electrostatics

10.2. Magnetostatics

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A.1. Lame coefficients

A.2. Some special orthogonal coordinates

A.3. Vector operations in orthogonal coordinates

A.4. Some explicit forms of vector operations

A.5. Relation between unit base vectors and their time derivatives

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Last update: April 5, 2017