Electromagnetic Field Theory Preliminary Examination Quiz

<p>6.28 mA</p> Signup and view all the answers

<p>$60a_x + 20a_y - 30a_z$ V/m, $-1.77 \times 10^{-8}$ C/m^2</p> Signup and view all the answers

<p>The physical significance of displacement current is that it represents the rate of change of electric displacement field in a region. It is given by the equation $I_d = \epsilon_0 A \frac{dE}{dt}$, where $I_d$ is the displacement current, $\epsilon_0$ is the permittivity of free space, $A$ is the area, and $\frac{dE}{dt}$ is the rate of change of electric field. Substituting the given values, $A = 10cm^2 = 10^{-3}m^2$, $d = 2mm = 2 \times 10^{-3}m$, $V = 300V$, and $f = 1MHz = 10^6Hz$, we can calculate the displacement current as $I_d = \epsilon_0 \times 10^{-3} \times \frac{300}{2 \times 10^{-3}} \times 2\pi \times 10^6 = 9.42mA$.</p> Signup and view all the answers

<p>Poisson's equation is given by $\nabla^2 \phi = -\frac{\rho}{\epsilon_0}$, where $\phi$ is the electric potential, $\nabla^2$ is the Laplacian operator, $\rho$ is the charge density, and $\epsilon_0$ is the permittivity of free space. Laplace's equation is a special case of Poisson's equation when $\rho = 0$, given by $\nabla^2 \phi = 0. These equations are fundamental in understanding the behavior of electric fields and potentials in different charge distributions and boundary conditions.</p> Signup and view all the answers

<p>The boundary condition between two perfect dielectric materials states that the normal component of the electric displacement field $D$ is continuous across the interface, i.e., $D_1^{\perp} = D_2^{\perp}$. This continuity of $D$ ensures that there are no free charges at the interface and the electric field lines terminate smoothly. The tangential component of the electric field $E$ may not be continuous across the interface due to the presence of surface charge density, but the normal component of $D$ remains continuous.</p> Signup and view all the answers

<p>To find the electric field $E$ and electric displacement field $D$ using the spherical coordinate system for the given concentric spherical shells with inner radius $a = 0.1m$ and outer radius $b = 0.2m$, we can use the relations $E = -\nabla \phi$ and $D = \epsilon E$, where $\phi$ is the electric potential and $\epsilon$ is the permittivity of the medium. The electric potential $\phi$ can be determined using the given potential differences and the fact that the medium between the shells is free space. Once $\phi$ is obtained, $E$ and $D$ can be calculated using the above relations.</p> Signup and view all the answers

<p>Displacement current density, denoted by $J_d$, is a term introduced by Maxwell in his modification of Ampère's law to account for the changing electric fields. It is given by the equation $J_d = \epsilon_0 \frac{\partial E}{\partial t}$, where $\epsilon_0$ is the permittivity of free space and $\frac{\partial E}{\partial t}$ is the time rate of change of the electric field. Its physical significance lies in its ability to create magnetic fields and contribute to electromagnetic wave propagation, even in regions where there is no actual current flow. This concept was crucial in the development of Maxwell's equations and the understanding of electromagnetic phenomena.</p> Signup and view all the answers