Electromagnetism Part-1

Explore scalar and vector fields in space, define temperature as a scalar field, and derive the gradient as a vector field that measures the maximum rate and direction of change.

Learn how outward flux through a closed surface defines divergence as the volume density of outward flux, derived from infinitesimal volumes and Gauss divergence theorem.

Explore line integrals of vector fields along paths, including closed-path circulation. Link circulation to curl via area vectors and the idea behind Stokes theorem.

Explore the fundamental theorems of gradient, divergence, and curl: gradient line integrals are path independent, Gauss's divergence theorem links flux to divergence, and Stokes theorem ties curl to boundary.

Delve into curvilinear coordinates, unit vectors, and scale factors; derive gradient, divergence, curl, and Laplacian, and learn transformations for spherical polar and cylindrical systems.

Explore how sources, charges at rest or in motion, create electric and magnetic fields, derive force on a test charge via Coulomb's law, and apply superposition to electrostatics.

Explores how identical charges at polygon vertices yield zero net force at the center by symmetry; also examines the z-axis field from two equidistant charges and the large-distance limit.

Apply the superposition principle and Coulomb's law to obtain the electric field from continuous charge distributions, using line, surface, and volume charge densities and vector calculus.

Learn how Gauss's law connects the flux of the electric field through closed surfaces to the net charge enclosed, independent of surface shape, via divergence and superposition.

Apply Gauss's law to open and closed surfaces, using symmetry to relate flux through surface parts to the total flux for various charge configurations.

Apply Gauss law to spherical and cylindrical symmetry, determine electric field directions, compute magnitudes from charges enclosed, and analyze fields inside and outside spheres and cylinders.

Learn to compute potentials for finite and infinite charge distributions, using path independence, reference points, and boundary conditions to relate inside and outside regions of shells, wires, and spheres.

Learn to compute electric fields and potentials from charge density through direct integration, Poisson’s equation, and Gauss’s law, while distinguishing finite and infinite distributions.

Explore work and energy in electrostatics: moving charges, external work, and the connection between potential, potential difference, and energy in point and continuous charge distributions.

Explore how a perfect conductor with unlimited free charge carriers rearranges charges to cancel internal fields, making the body equipotential and causing surface charges and induced charges.

Use the method of images to solve Poisson’s equation above a grounded plane, yielding V=(q/4πϵ0)(1/r_+−1/r_−) and the induced sigma(r)=−(q d)/(2π(r^2+d^2)^(3/2)) with total −q.

Explore the multipole expansion of electrostatic potential, identifying when monopole, dipole, or quadrupole terms dominate at large distances and how dipole moment depends on origin.

Explore how neutral atoms polarize in an electric field, inducing dipole moments and illustrating atomic polarization with crude atomic models and the relation between dipole moments and applied fields.

Explore magnetic fields from current-carrying wires and the Lorentz force on moving charges. See cyclotron and helix motions, and relate them to momentum and cyclotron frequency.

Explore the motion of a charged particle in perpendicular electric and magnetic fields, revealing a cycloid trajectory in the z-y plane, governed by v cross B and cyclotron frequency.

In a magnetic field, moving charges experience the Lorentz force q v × B, producing current I; the lecture defines line, surface, and volume current densities k and J.

Derive the continuity equation from charge conservation and relate surface current to the rate of change of enclosed charge. Introduce Biot-Savart law, steady current, and current enclosed by a path.

Explore Ampere's law with circular loops, relate line integrals to current enclosed, and derive the magnetic field of a long straight wire, highlighting surface choices and current continuity.

Explore how current direction along z or phi affects the magnetic field direction, illustrated by solenoid configurations, to solidify the current-field relationship in electromagnetism.

Explore Ampere's law through Problem 5.14 and Problem 5.15, analyzing magnetic fields and the integral form in this 2024 discussion.

Explore how magnetic forces do not work on moving charges, why batteries supply work instead, and how symmetry and line-integral reasoning explain fields inside and outside very long solenoids.

Explore how rotating charges generate magnetic dipole moments from current loops and spinning objects, and relate these moments to orbital and spin angular momentum.

Explore electromotive force and the line integral around a circuit, separating source and electric-field effects, with emphasis on battery regions, potential difference, and the static closed-loop condition.

Explore how changing magnetic flux induces current in a loop, governed by Faraday's law and Lenz's law, with surfaces and motion revealing the direction and magnitude of induction.

Examine how changing currents produce magnetic flux and energy in magnetic fields, analyze inductance and mutual inductance, and apply Maxwell's equations to LC circuits.

Study a coaxial cylinder with surface currents, deriving the magnetic field between cylinders via Ampere's law and boundary conditions. Connect the analysis to Maxwell's equations, displacement current, and continuity equation.