Electromagnetic Theory I
Electrostatics and magnetostatics developed from their field equations with the full tools of vector calculus: why electromagnetism is written in terms of fields, superposition and a preview of Maxwell's equations; gradient, divergence, curl, the Laplacian, product rules and the divergence and Stokes theorems, checked numerically; spherical and cylindrical coordinates, the Dirac delta function and the Helmholtz theorem; Gauss's law in differential and integral form derived from Coulomb's law, fields of symmetric distributions and the boundary conditions at a surface charge; the electric potential, Poisson's and Laplace's equations and the energy stored in the field; conductors, shielding, charge on curved surfaces, capacitance of plates, spheres and coaxial cables, and electrostatic pressure; harmonic functions, Earnshaw's theorem, the uniqueness theorems, the method of images for planes and spheres and the numerical solution of Laplace's equation by successive over-relaxation; separation of variables in Cartesian and spherical coordinates, Legendre polynomials and the multipole expansion; polarization, bound charge, the displacement field, linear dielectrics and a dielectric sphere in a uniform field; the Lorentz force, the Biot–Savart law, Ampère's law, Helmholtz coils and the divergence and curl of the magnetic field; the vector potential, gauge freedom, magnetic boundary conditions and the magnetic dipole, including the Earth's field; and a capstone on magnetization, bound currents, the auxiliary field H, diamagnetism, paramagnetism, ferromagnetism and hysteresis, with transformer cores, superconducting MRI magnets and the Meissner effect, all supported by runnable Python examples.
PHYS-381 Year 3 3 credits 12 lessons · 4 h 33 min ▶ Video lessons coming soon
Offered by HSM University · Physics
This is the Canadian version of this course. See the American version.
What you'll learn
- Explain why electromagnetism is formulated in terms of fields, apply superposition to point and continuous charge distributions, and state the static Maxwell equations.
- Compute gradients, divergences, curls and Laplacians, interpret them physically, and apply the divergence theorem and Stokes' theorem.
- Work in spherical and cylindrical coordinates and use the Dirac delta function to represent point, line and surface charges, including \(\nabla\cdot(\hat{\mathbf{r}}/r^2) = 4\pi\delta^3(\mathbf{r})\).
- Derive \(\nabla\cdot\mathbf{E} = \rho/\varepsilon_0\) and \(\nabla\times\mathbf{E} = \mathbf{0}\) from Coulomb's law, and use Gauss's law to find fields of symmetric charge distributions.
- Define the electric potential, derive Poisson's and Laplace's equations, compute potentials of charge distributions, and calculate electrostatic energy from charges or from the field.
- Apply the properties of conductors, the boundary conditions at surfaces and the concept of capacitance, including energy and forces on conductors.
- Use the mean value property, Earnshaw's theorem and the uniqueness theorems, solve problems by the method of images, and solve Laplace's equation numerically by relaxation.
- Solve Laplace's equation by separation of variables in Cartesian and spherical coordinates and expand potentials in multipoles using Legendre polynomials.
- Describe polarization and bound charge, use the displacement field and linear dielectrics, and solve problems with dielectric boundaries.
- Apply the Lorentz force law, the Biot–Savart law and Ampère's law, and derive \(\nabla\cdot\mathbf{B} = 0\) and \(\nabla\times\mathbf{B} = \mu_0\mathbf{J}\).
- Use the magnetic vector potential, gauge freedom and the magnetic boundary conditions, and describe the magnetic dipole and its far field.
- Describe magnetization, bound currents and the auxiliary field H, explain diamagnetism, paramagnetism, ferromagnetism and hysteresis, and analyse transformer cores, MRI magnets and superconductors.
Course content
12 lessons · 4 h 33 min total · final exam
- 1 Why electromagnetic theory: fields as the language of physics 22 min · quiz
- 2 Vector calculus for electromagnetism: gradient, divergence, curl and the theorems 23 min · quiz
- 3 Curvilinear coordinates and the Dirac delta function 26 min · quiz
- 4 Electrostatics: Coulomb's law, Gauss's law and the electric field 22 min · quiz
- 5 The electric potential and electrostatic energy 24 min · quiz
- 6 Conductors, capacitance and boundary conditions 22 min · quiz
- 7 Laplace's equation, uniqueness and the method of images 21 min · quiz
- 8 Separation of variables and the multipole expansion 23 min · quiz
- 9 Electric fields in matter: polarization, dielectrics and the displacement field 21 min · quiz
- 10 Magnetostatics: the Lorentz force, Biot–Savart and Ampère's law 23 min · quiz
- 11 The vector potential and magnetic boundary conditions 23 min · quiz
- 12 Capstone: magnetic fields in matter and applications 23 min · quiz
- E Final exam 20 questions
Requirements
Recommended background. You can start any course at any time.
Description
Electrostatics and magnetostatics developed from their field equations with the full tools of vector calculus: why electromagnetism is written in terms of fields, superposition and a preview of Maxwell's equations; gradient, divergence, curl, the Laplacian, product rules and the divergence and Stokes theorems, checked numerically; spherical and cylindrical coordinates, the Dirac delta function and the Helmholtz theorem; Gauss's law in differential and integral form derived from Coulomb's law, fields of symmetric distributions and the boundary conditions at a surface charge; the electric potential, Poisson's and Laplace's equations and the energy stored in the field; conductors, shielding, charge on curved surfaces, capacitance of plates, spheres and coaxial cables, and electrostatic pressure; harmonic functions, Earnshaw's theorem, the uniqueness theorems, the method of images for planes and spheres and the numerical solution of Laplace's equation by successive over-relaxation; separation of variables in Cartesian and spherical coordinates, Legendre polynomials and the multipole expansion; polarization, bound charge, the displacement field, linear dielectrics and a dielectric sphere in a uniform field; the Lorentz force, the Biot–Savart law, Ampère's law, Helmholtz coils and the divergence and curl of the magnetic field; the vector potential, gauge freedom, magnetic boundary conditions and the magnetic dipole, including the Earth's field; and a capstone on magnetization, bound currents, the auxiliary field H, diamagnetism, paramagnetism, ferromagnetism and hysteresis, with transformer cores, superconducting MRI magnets and the Meissner effect, all supported by runnable Python examples.
Part of the Science stream, typically taken in year 3.