3. Consider a square waveguide of side 2L, centered at the origin, with axis running parallel...
4. Consider the cylindrical waveguide below, which has an electromagnetic wave propagating in the space between the inner and outer conductors, which is a gap where air exists. The radius of the inner conductor is a, while the inner radius of the outer conductor is b (as shown). The fields in the air-gap have the form E = E0r cos (kz z ωt) B = B0r cos (kz z ωt) where E0 and B0 are constants, r is the radial...
[132 2 2 3 4 17 marks] Question 4 A plane wave is travelling in a vacuum in the +z-direction with wavenumber k and angular frequency . It is linearly polarised in the x-direction, and has electric field given by E(t, z) Eo Cos(kz - wt)f This wave is normally incident on a perfectly electrically conducting, semi-infinite slab in the region z > 0 and the resulting field in vacuum (z < 0) is a superposition of the incident and...
Consider a sphere centered at the origin of radius 1 that rotates about the z-axis in a "west to east" direction with constant angular speed . Suppose that an ant travels "north" on the sphere with angular speed and is located at (1,0,0) at time t=0. Then the position of the ant can be given by for . Compute the acceleration and show that it can be written as where, , . We were unable to transcribe this imageWe were...
Electromagnetic waves transport energy. This problem shows you which parts of the energy are stored in the electric and magnetic fields, respectively, and also makes a useful connection between the energy density of a plane electromagnetic wave and the Poynting vector. In this problem, we explore the properties of a plane electromagnetic wave traveling at the speed of light c along the x axis through vacuum. Its electric and magnetic field vectors are as follows: E = E, sin (kx...
2. A long solenoid carrying a time-dependent current I(t) is wound on a hollow cylinder whose axis of symmetry is the z-axis. The solenoid's radius is a, and it has n turns per metre. (a) * Write down the magnetic intensity H(ที่ t) and magnetic field B(r,t) everywhere. What is the energy density in the magnetic field inside the solenoid? (b Find the electric field E(F,t) everywhere using Faraday's law in integral form. (c) * Find the magnetic vector potential...
xzontal, circular, loop is in a magnetic field parallel to plane of the loop. The loop has a current in it. which way, if any, does the loop rotate? It is fixed so that it can only rotate about the axis shown. B - 2.00 T 1.50 A R-0.750 m axis of rotation (a) What is the orientation energy of the loop if it is rotated with side u straight up and side b straight down? 2. A square loop...
Consider our standard coax cable as an “infinite” length wire of radius a surrounded by a thin conducting cylinder, coaxial with the wire, with inner radius b and outer radius c. Again, assume ab and cbb (thin shell and wire), as show in the figure. We now want to investigate energy flow in the same cylindrical coax cable defined above. However, for now, let’s just look at fields constant in time, not varying in time. Assume that constant current I...
I've already solved other problems except (d). Although I cannot understand (d). Please solve (d) and give me a detailed explanation. -------------------------------------------- This is the real problem. I posted a wrong problem. please solve this problem. sorry. What are the instantaneous and time-averaged torque under this condition? 4.30 Figure 4.42 shows in schematic cross section a salient-pole synchronous machine having two identical stator windings a and b on a laminated steel core. The salient-pole rotor is made of steel and...
Consider a cylindrical capacitor like that shown in Fig. 24.6. Let d = rb − ra be the spacing between the inner and outer conductors. (a) Let the radii of the two conductors be only slightly different, so that d << ra. Show that the result derived in Example 24.4 (Section 24.1) for the capacitance of a cylindrical capacitor then reduces to Eq. (24.2), the equation for the capacitance of a parallel-plate capacitor, with A being the surface area of...
please answer question 8-13 This is the prior information: Nerve impulses are electrical currents in the form of “ionic flows.” Therefore the electrical properties of the axon are important to understand in order to understand the flow of electrical impulses. In this test, you will explore the capacitance and resistivity of an axon of a nerve cell. For this test, the axon will be treated as a CYLINDER of arbitrary length “L” and radius “a” that is filled with a...