Electric Force and Field Theory Concepts

The vector form of Coulomb's law states that the electric force $ extbf{F}$ between two point charges is given by $ extbf{F} = k rac{Q_1 Q_2}{r^2} extbf{r}$, where $k$ is Coulomb's constant, $Q_1$ and $Q_2$ are the point charges, $r$ is the distance between them, and $ extbf{r}$ is the unit vector pointing from one charge to the other.

The divergence theorem states that the integral of the divergence of a vector field over a volume is equal to the flux of the vector field through the closed surface surrounding the volume, expressed mathematically as $ abla ullet extbf{F} , dV = extbf{F} ullet d extbf{A}$.

Wave propagation in a good conductor is significant because it determines how electromagnetic waves are attenuated and distributed within the material, affecting energy loss and signal integrity.

<p>Transverse magnetic (TM) mode refers to a wave propagation mode in which the magnetic field has no component in the direction of wave propagation, meaning the electric field is transverse to the direction of wave travel.</p> Signup and view all the answers

<p>The standing wave ratio (SWR) can be calculated as $SWR = rac{1 + |eta|}{1 - |eta|}$, where $eta$ is the reflection coefficient. With the given impedances, the calculation yields an SWR of approximately 1.5.</p> Signup and view all the answers

<p>Biot-Savart's law describes the magnetic field $ extbf{B}$ generated by a current-carrying conductor, stating that $d extbf{B} = rac{rac{ ext{μ}_0 I}{4 ext{π}} d extbf{l} imes extbf{r}}{r^3}$, where $I$ is the current, $d extbf{l}$ is the length element of the wire, and $ extbf{r}$ is the distance from the wire to the point of interest.</p> Signup and view all the answers

<p>Characteristic impedance is defined as $Z_0 = rac{V}{I}$ in a transmission line, characterizing the relationship between voltage and current waves traveling along the line. It determines how much of the incident power is reflected or transmitted when encountering a load impedance.</p> Signup and view all the answers

<p>The input impedance $Z_{in}$ for a quarter-wave transmission line is calculated as $Z_{in} = rac{Z_0^2}{Z_1}$, leading to values of 0 for $Z_1 = 0$, infinite for $Z_1 = ext{∞}$, and 60Ω for $Z_1 = 60Ω$.</p> Signup and view all the answers

<p>La constante de propagation est une mesure qui décrit comment un signal se propage le long d'une ligne de transmission, incluant l'atténuation et la phase.</p> Signup and view all the answers

<p>Le circuit équivalent d'une ligne de transmission comprend la résistance (R), l'inductance (L), la conductance (G) et la capacité (C) par unité de longueur.</p> Signup and view all the answers

<p>La constante de propagation aide à comprendre comment les signaux se déforment et s'atténuent au fur et à mesure de leur propagation sur la transmission.</p> Signup and view all the answers

<p>Une constante de propagation élevée peut entraîner une plus grande réflexion des signaux, surtout si l'impédance de charge diffère de l'impédance caractéristique.</p> Signup and view all the answers

<p>L'impédance caractéristique affecte la vitesse de propagation des ondes le long de la ligne et détermine les conditions de terminaison nécessaires pour minimiser les réflexions.</p> Signup and view all the answers