Electromagnetic Field Theory & Transmission Lines

Explore Coulomb's law: the force between two charges is proportional to Q1 Q2 and inversely proportional to the square of their distance, along the line joining them.

Extend Coulomb's law to two charges, showing electrostatic force acts along the line joining them, repulsive for like charges and attractive for opposite charges, along the unit vector between them.

Apply Coulomb's law to compute the force between two point charges Q1 and Q2 separated by r. Use the unit vector along the line joining them and r^2 for calculation.

Apply coulomb's law to a system of charges using the superposition principle. Compute each inter-charge force and sum vectorially to find the net force on a selected charge.

Explore the electric field as a physical quantity and its intensity, and the force on a test charge, showing how field strength depends on distance, charge, and voltage.

Apply Coulomb’s law to a system of charges to calculate the electric field and forces, using superposition to sum contributions and note limits at high frequency.

Explore electric field lines and their properties, including outward direction from positive charges and inward toward negative charges, their non-crossing nature, and the concept of a uniform electric field.

Explore line integrals in electromagnetic fields by summing differential elements along a path, projecting onto the tangential direction to obtain the physical quantity.

Explore surface and volume integrals, and how flux through open or closed surfaces relates to vector fields, normals, and differential elements, with applications to divergence and boundary concepts.

Explore continuous charge distributions, including line, surface, and volume, define differential elements and charge densities, and compute total charge by integrating across each distribution.

Explore how electric field intensity arises from line and surface charge distributions, using differential elements and densities to derive line and surface field formulas.

Explore electric flux lines around charges, how field lines radiate outward or inward, and how the electric flux equals the enclosed charge.

Explore the electric flux density and how flux through a surface depends on the normal to the surface and the area, revealing the total flux behavior.

Compute the electric flux density using differential surface area, accounting for the surface normal and angle between the surface and the field, and understand how flux changes with orientation.

Explore electric flux density for line, surface, and volume charge distributions using Gauss's law. Learn how permittivity in free space shapes field intensity and the relation between flux and charge.

Explore Gauss law, the relation between the flux through a closed surface and the enclosed charge, and its link to Maxwell's first equation in integral form.

Gauss's theorem demonstrates the relation between the electric flux through a closed surface and the enclosed charge, using the point-charge field and surface integrals.

Explore the continuity variation for time varying fields, deriving the continuity equation from the net current through a surface, and relate surface integral to conservation under the law of conservation.

Understand relaxation time, the period in which a material's value decays to 36.8% of its initial value. Relate this decay to Maxwell's equations, the permittivity epsilon, and the conductivity sigma.

Explore electric potential as the work required to move a unit charge from infinity to a point in a field, linking work, charge, and potential difference.

Calculate the electric potential at a point by summing each charge's contribution, using distances to each charge (r1, r2, r3) and the expression V = k(q1/r1 + q2/r2 + q3/r3).

Learn how Maxwell's equations relate the electric field direction to work and motion, and how a line integral can be rewritten as a surface integral, connecting line and surface viewpoints.

Examine the relation between E and H by deriving the total differential of the space-dependent potential in three-dimensional Cartesian coordinates, showing how V varies with x, y, and z.

Compute the energy density and energy storage of an electrostatic field by assembling charges from infinity, and relate it to the work done and resulting potentials.

Derive the electrostatic energy density and total energy from Maxwell equations, using vector identities to show W = 1/2 ∫ ε E^2 dτ for line, surface, and volume charge configurations.

Uncover the Poisson equation and its use to find potential at the boundary, and relate the electric field to the potential through epsilon.

Explore the Laplace equation and its three types of solutions, and derive their forms in rectangular (Cartesian) and cylindrical coordinate systems.

The uniqueness theorem asserts that with identical boundary conditions, the governing equation has a single solution; by comparing two solutions and analyzing their difference, we show this difference must vanish.

Explore magnetostatics and static magnetic fields produced by currents and permanent magnets. Learn the right-hand rule, magnetic field intensity H, and magnetic flux density B with permeability relations.

Apply Biot–Savart law to calculate the magnetic field intensity from a current element, using dH ∝ I dl × r̂ / R^2 and integrating over line and surface elements.

Apply Ampere's circuital law to an infinite long conductor using a circular path, relating the line integral of magnetic field intensity to the enclosed current.

Prove Ampere's circuital law by showing line integral of magnetic field intensity around a loop equals enclosed current, using Stokes' theorem to relate line and surface integrals in Maxwell's equations.

Investigate the magnetic field H from an infinite sheet current using the right-hand rule and Ampere’s law, arising from the surface current density.

Explore magnetic flux density, magnetic flux, and magnetic field intensity, and relate surface and volume integrals to one of Maxwell's equations.

Explore magnetic force from moving charges and current elements. Derive the cross-product relation F = q v × B and contrast magnetic and electric forces within the electromagnetic field.

Explains Faraday's law, distinguishing electrostatic and motional emf, and shows how changing magnetic flux induces emf in circuits, with stationary and moving loop scenarios.

Explore how a moving conductor in a magnetic field induces emf, leading to transformer action, with line and surface integral formulations that relate emf to changing magnetic field.

Move a current loop in a magnetic field to cut field lines, create a motional electric field, and induce emf, linking transformer emf with motional emf through flux.

Explore emf induction by moving and stationary loops in time-varying magnetic fields, deriving emf from the rate of change of flux linkage, and analyzing transformer and motional emf.

Explore how Ampere's law is modified for time-varying fields by introducing displacement current, reconciling conduction currents with the continuity equation, and presenting Maxwell-Ampere corrections.

Explore displacement current density and conduction current, and see how capacitance relates to area, distance, and epsilon, linking displacement current to current continuity.

Analyze the magnetic force on a differential current element and compare ideal versus real class B line elements and surface elements, using integration.

Explain the amperes force law between two current-carrying conductors, the magnetic field from current elements, and how parallel currents attract while opposite directions repel.

Explore the four Maxwell equations in differential and integral forms, linking electric displacement, charge, current, and magnetic fields to static and time-varying electromagnetic phenomena.

Explore Maxwell equations for time-varying fields, covering Gauss's law, Faraday's law, and Ampere's law with displacement current, and explain magnetic flux density and the absence of magnetic monopoles.

Learn Maxwell's equations for sinusoidal field variations and derive their integral forms. Apply these four integral equations to analyze electromagnetic fields in practical transmission-line scenarios.

Learn how electromagnetic waves propagate as oscillating electric and magnetic fields traveling through media, using modulation techniques that combine high and low frequency signals from a transmitter.

This lecture derives the wave equation for a lossless delta by modifying Maxwell’s equations, applying derivatives, and interpreting source terms with electric and magnetic components.

Derive the wave equations for electric and magnetic fields in a lossless conducting medium from Maxwell's equations, using epsilon, mu, and sigma.

Derive the electromagnetic wave equation in phasor form and compute time-dependent fields using frequency and amplitudes. Apply free-space propagation concepts to connect theory with field behavior.

Explore the electromagnetic wave equation for a conducting medium, compare with free-space form, and show how epsilon, mu, sigma shape propagation and attenuation through omega and gamma.

Investigate wave propagation in a lossless medium, derive the differential equation, and obtain traveling wave solutions in x using the real part of complex exponentials for forward and backward directions.

Derive the wave equation for a lossless conducting medium and analyze the propagation constant gamma, highlighting how alpha and beta govern amplitude and phase along the x direction.

derive the attenuation constant alpha and the phase constant beta from the complex propagation constant gamma in a lossy medium, showing gamma's square-root relationship to omega, mu, sigma, and epsilon.

Analyze how conductors and dielectrics respond at different frequencies, using sigma, omega, and epsilon to understand depth of penetration and loss tangent, and distinguish good conductors from dielectrics.

explains the electromagnetic wave equation in a good dielectric, deriving expressions with epsilon, sigma, and omega and showing square-root simplifications of combined terms.

Explore electromagnetic wave characteristics in a good conductor, deriving the attenuation constant alpha and the propagation constant gamma from sigma, omega, mu, and epsilon, especially when sigma dominates omega epsilon.

Explore wave propagation in good conductors, linking intrinsic impedance and phase velocity to conductivity, and show how increasing conductivity reduces velocity and increases energy loss.

Understand how skin depth confines current to the conductor's outer surface at high frequencies, reducing amplitude to about 36.8% of its value via exponential attenuation.

Explore the uniform plane wave, where electric and magnetic fields are perpendicular and constant in amplitude, propagate in a direction, and obey a fixed frequency via intrinsic impedance.

Explore the characteristics of a uniform plane wave traveling in the x direction, with electric and magnetic field components perpendicular to the propagation and governed by Maxwell equations.

Explore the polarization of a uniform plane wave, including linear, horizontal, vertical, circular, and elliptical polarization, and how fixed time snapshots reveal the electric field orientation and phase relationships.

Learn how transmission lines transfer information in communication systems, from wireless links using transmitter, antenna, and receiver to wired options like coaxial cables, twisted pairs, power lines, and optical fibre.

Explore the transmission line concept through its per-unit-length model using R, L, G, and C, and learn how these primary constants define energy transfer, losses, and circuit behavior.

Derive the transmission line equations for two parallel conductors, linking voltage and current through a second-order differential equation, and introduce the propagation constant gamma with exponential solutions along the line.

Derive the transmission line equations and solve for the constants A and B using gamma and x, applying boundary conditions to relate voltage and current along the line.

Explore the infinite transmission line, where voltage and current decay exponentially with distance due to attenuation, described by the transmission line differential equations and a propagation constant gamma.

Explore the characteristic impedance as the input impedance of infinite transmission lines, and relate it to voltage, current, and the propagation constant.

Analyze the characteristic impedance for a finite-length transmission line, derive the input impedance and reflection conditions from the transmission-line equations, and examine termination effects.

Explain the lossless transmission line by reviewing resistance, conductance, and capacitance and their primary constants, and show how the propagation constant alpha and beta relate to losses.

Explore how a distortionless transmission line preserves signal integrity by satisfying the distortion-reducing condition Arbidol equals to GBC across multiple frequency components, ensuring output matches input.

Explore how distortions arise in transmission lines from multiple frequencies and impedance mismatches, and how attenuation and propagation constants (alpha, beta, omega, L, C) shape the output signal.

Explore the input impedance of a lossless transmission line under open-circuit and short-circuit terminations, deriving how termination conditions affect impedance via the reflection coefficient gamma.

investigate the input impedance of a lossy transmission line under open-circuit and short-circuit conditions, and relate the propagation constant gamma to the lossless case, highlighting alpha and beta relationships.

Investigate the input impedance of a lossless transmission line, focusing on open-circuit and short-circuit configurations and how line conditions affect impedance.

Explore reflection coefficient in transmission line theory, deriving how load termination affects incident and reflected waves, and analyze open, short, and matched terminations to predict standing waves.

Explore standing wave formation on transmission lines, derive standing wave ratio and reflection coefficient, and relate SWR and VSWR to incident and reflected waves.