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- https://phys.libretexts.org/Bookshelves/Electricity_and_Magnetism/Electromagnetics_II_(Ellingson)/12%3A_Mathematical_Formulas/12.03%3A_Vector_Identities\[ \begin{align} \nabla \cdot ( \nabla \times \mathbf { A } ) &= 0\\[5pt] \nabla \times ( \nabla f ) &= 0\\[5pt] \nabla \times ( f \mathbf { A } ) &= f ( \nabla \times \mathbf { A } ) + ( \nabla f ) \...\[ \begin{align} \nabla \cdot ( \nabla \times \mathbf { A } ) &= 0\\[5pt] \nabla \times ( \nabla f ) &= 0\\[5pt] \nabla \times ( f \mathbf { A } ) &= f ( \nabla \times \mathbf { A } ) + ( \nabla f ) \times \mathbf { A }\\[5pt] \nabla \cdot ( \mathbf { A } \times \mathbf { B } ) &= \mathbf { B } \cdot ( \nabla \times \mathbf { A } ) - \mathbf { A } \cdot ( \nabla \times \mathbf { B } )\\[5pt] \nabla \cdot ( \nabla f ) &= \nabla ^ { 2 } f\\[5pt] \nabla \times \nabla \times \mathbf { A } &= \nabla…
- https://phys.libretexts.org/Bookshelves/Electricity_and_Magnetism/Electromagnetics_II_(Ellingson)/05%3A_Wave_Reflection_and_Transmission/5.06%3A_Plane_Waves_at_Oblique_Incidence_on_a_Planar_Boundary-_TE_Case\[\hat{\bf y}E^i_{TE}e^{-j{\bf k}^i\cdot{\bf r}_0} + \hat{\bf y}B e^{-j{\bf k}^r\cdot{\bf r}_0} = \hat{\bf y}C e^{-j{\bf k}^t\cdot{\bf r}_0} \label{m0167_eBCE} \] \[\hat{\bf x}\cdot\widetilde{\bf H}^i...\[\hat{\bf y}E^i_{TE}e^{-j{\bf k}^i\cdot{\bf r}_0} + \hat{\bf y}B e^{-j{\bf k}^r\cdot{\bf r}_0} = \hat{\bf y}C e^{-j{\bf k}^t\cdot{\bf r}_0} \label{m0167_eBCE} \] \[\hat{\bf x}\cdot\widetilde{\bf H}^i({\bf r}_0) + \hat{\bf x}\cdot\widetilde{\bf H}^r({\bf r}_0) = \hat{\bf x}\cdot\widetilde{\bf H}^t({\bf r}_0) \nonumber \]
- https://phys.libretexts.org/Bookshelves/Electricity_and_Magnetism/Electromagnetics_I_(Ellingson)/04%3A_Vector_Analysis/4.01%3A_Vector_ArithmeticIn mathematical notation, a real-valued vector A is said to have a magnitude A=|A| and direction a^ such that A=Aa^(4.1.1) where a^ is a unit vector (i.e., a real-valued vector having magnitud...In mathematical notation, a real-valued vector A is said to have a magnitude A=|A| and direction a^ such that A=Aa^(4.1.1) where a^ is a unit vector (i.e., a real-valued vector having magnitude equal to one) having the same direction as A . If a vector is complex-valued, then A is similarly complex-valued
- https://phys.libretexts.org/Bookshelves/Electricity_and_Magnetism/Electromagnetics_I_(Ellingson)/02%3A_Electric_and_Magnetic_Fields/2.04%3A_Electric_Flux_DensityElectric flux density, assigned the symbol D , is an alternative to electric field intensity ( E ) as a way to quantify an electric field.
- https://phys.libretexts.org/Courses/Berea_College/Electromagnetics_I/03%3A_Transmission_Lines/3.01%3A_Introduction_to_Transmission_LinesTransmission lines are designed to support guided waves with controlled impedance, low loss, and a degree of immunity from EMI.
- https://phys.libretexts.org/Bookshelves/Electricity_and_Magnetism/Electromagnetics_I_(Ellingson)/05%3A_Electrostatics/5.20%3A_Dielectric_MediaDielectric is particular category of materials that exhibit low conductivity because their constituent molecules remain intact when exposed to an electric field, as opposed to shedding electrons as is...Dielectric is particular category of materials that exhibit low conductivity because their constituent molecules remain intact when exposed to an electric field, as opposed to shedding electrons as is the case in good conductors. Subsequently, dielectrics do not effectively pass current, and are therefore considered “good insulators” as well as “poor conductors.” An important application of dielectrics in electrical engineering is as a spacer material in printed circuit boards & coaxial cables.
- https://phys.libretexts.org/Bookshelves/Electricity_and_Magnetism/Electromagnetics_I_(Ellingson)/03%3A_Transmission_Lines/3.13%3A_Standing_WavesA standing wave consists of waves moving in opposite directions. These waves add to make a distinct magnitude variation as a function of distance that does not vary in time.
- https://phys.libretexts.org/Bookshelves/Electricity_and_Magnetism/Electromagnetics_I_(Ellingson)/10%3A_Appendices/10.05%3A_Mathematical_Formulas_-_Vector_OperatorsThis section contains a summary of vector operators expressed in each of the three major coordinate systems:
- https://phys.libretexts.org/Bookshelves/Electricity_and_Magnetism/Electromagnetics_I_(Ellingson)/07%3A_Magnetostatics/7.11%3A_Boundary_Conditions_on_the_Magnetic_Field_Intensity_(H)In homogeneous media, electromagnetic quantities vary smoothly and continuously. At a boundary between dissimilar media, however, it is possible for electromagnetic quantities to be discontinuous. Con...In homogeneous media, electromagnetic quantities vary smoothly and continuously. At a boundary between dissimilar media, however, it is possible for electromagnetic quantities to be discontinuous. Continuities and discontinuities in fields can be described mathematically by boundary conditions and used to constrain solutions for fields away from these boundaries. In this section, we derive boundary conditions on the magnetic field intensity H .
- https://phys.libretexts.org/Bookshelves/Electricity_and_Magnetism/Electromagnetics_I_(Ellingson)/05%3A_Electrostatics/5.04%3A_Electric_Field_Due_to_a_Continuous_Distribution_of_ChargeIt is common to have a continuous distribution of charge as opposed to a countable number of charged particles. In this section, we extend the discrete perspective of charge distributions into the con...It is common to have a continuous distribution of charge as opposed to a countable number of charged particles. In this section, we extend the discrete perspective of charge distributions into the concept of continuous distribution of charge so that we may address this more general class of problems.
- https://phys.libretexts.org/Bookshelves/Electricity_and_Magnetism/Electromagnetics_I_(Ellingson)/03%3A_Transmission_Lines/3.03%3A_Transmission_Lines_as_Two-Port_Devices(unable to fetch text document from uri [status: 403 (Forbidden)])
