PU-102 · Electricity & Magnetism I
Starting from the empirical Coulomb and Ampère force laws, the unit builds the classical electromagnetic field concept in stages — electrostatics, steady currents, and magnetostatics — culminating in the pre-Maxwell field equations and their potential formulation. The arc is deliberately constructive: every field theorem (Gauss, Ampère, the boundary conditions, the energy density) is proved from the underlying force law and vector calculus, so that PU-202 can later close the loop into the full Maxwell equations and electromagnetic waves.
Lectures
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Derivations homed in this unit
Electric Field from Coulomb's Law
Defines the electrostatic field as the force per unit test charge and expresses it as a superposition integral over a charge distribution.
Gauss's Law (Integral Form) from Coulomb
Shows that the flux of the Coulomb field through any closed surface equals the enclosed charge over epsilon-zero, using the solid-angle subtended by the surface.
Differential Gauss's Law via the Divergence Theorem
Converts the integral flux law into the local statement that the divergence of E equals charge density over epsilon-zero.
Irrotationality of the Electrostatic Field
Proves that the curl of the electrostatic field vanishes because the Coulomb field is a gradient, making it conservative.
Scalar Potential, Poisson and Laplace Equations
Introduces the electrostatic potential from the irrotational field and derives Poisson's equation and its source-free Laplace limit.
Uniqueness Theorem for Boundary-Value Problems
Proves that a solution of Poisson's equation satisfying given Dirichlet or Neumann boundary data is unique, justifying the method of images.
Electrostatic Energy and Field Energy Density
Computes the work to assemble a charge distribution and rewrites it as an integral of epsilon-zero-over-two times E-squared, locating energy in the field.
Fields at Conductor Surfaces
Derives that the field inside a conductor vanishes, is normal at the surface, and has magnitude sigma over epsilon-zero, with the surface an equipotential.
Multipole Expansion of the Potential
Expands the potential of a bounded charge distribution in inverse powers of distance, identifying monopole, dipole, and quadrupole terms via Legendre polynomials.
Dielectrics, Bound Charge and the D Field
Shows that polarization produces bound volume and surface charge and leads to the auxiliary field D obeying Gauss's law with only free charge.
Continuity Equation and Charge Conservation
Derives the local conservation law relating the divergence of current density to the time rate of change of charge density.
Biot–Savart Law from the Current Force Law
Establishes the magnetic field of a steady current element as an inverse-square, transverse field from the force between current elements.
Absence of Magnetic Monopoles
Proves that the divergence of the Biot–Savart field vanishes identically, so magnetic field lines never begin or end.
Ampère's Circuital Law from Biot–Savart
Derives that the curl of the magnetostatic field equals mu-zero times current density, equivalently the line integral equals the enclosed current.
Magnetic Vector Potential and Gauge Freedom
Introduces A from the divergence-free B field, shows gauge freedom, and reduces Ampère's law to a Poisson equation in the Coulomb gauge.
Magnetic Dipole: Field, Torque and Energy
Derives the far field, the torque, and the potential energy of a current loop in a magnetic field, defining the magnetic moment.
Lorentz Force and Cyclotron Motion
Combines the electric and magnetic forces on a moving charge and solves the equation of motion for helical cyclotron trajectories.
Magnetized Matter, Bound Currents and H
Shows that magnetization produces bound volume and surface currents and leads to the auxiliary field H obeying Ampère's law with only free current.
Ohm's Law, Resistance and Kirchhoff's Rules for DC Circuits
Integrating J = sigma E over a wire gives V = IR with R = rho L/A; charge conservation and curl E = 0 give Kirchhoff's junction and loop rules.
The RC Circuit: Charging, Discharging and the Time Constant
Kirchhoff's loop rule makes an RC circuit a first-order ODE: charge rises and falls exponentially with time constant RC, and half the energy is lost in R.