Derive the electric and magnetic fields radiated by an electric Hertz (infinitesimal) dipole
Derive the electric and magnetic fields radiated by an electric Hertz (infinitesimal) dipole
Problem 2 An infinitesimal electric dipole is centered at the origin and lies on the x-y plane along a line which is at an angle of 45 degrees with respect to the x-axis. Find the far-zone electric and magnetic fields radiated. The answer should be a function of spherical coordinates.
1. 135 points] A horizontal infinitesimal electric dipole of a constant current I, has the length, I is placed symmetrically about the origin, and directed along the x-axis. Derive the (a) Far-zone fields radiated by the dipole. (b) Plot radiation patterns in the ф-0° and ф-900 planes. (c) Calculate the polarization of the dipole at a point P(r, θ-60°, φ-0°) (d) Show that its maximum directivity, Do 1.5.
Only 4.10 (b) using the vector potential approach... Thank
you!
14.9. An infinitesimal magnetic dipole of constant current ,,, and length I is symmetrically placed about the origin along the z-axis. Find the (a) spherical E- and H-field components radiated by the dipole in all space (b) directivity of the antenna 10. For the infinitesimal magnetic dipole of Problem 4.9, find the far-zone fields when the element is placed along the (b) y-axis
Using the vector potential A and the procedure outlined in Section 3.6 of Chapter 3, derive the far-zone spherical electric and magnetic field components of a horizontal infinitesimal dipole placed at the origin of the coordinate system of Figure 4.1 Solution: Using (4-4), but for a horizontal infinitesimal dipole of uniform current directed along the y-axis, the corresponding vector potential can be written as uloleikr A = â 4πη with the corresponding spherical components, using the rectangular to spherical components...
8. [8 pts] Crossed electric and magnetic fields are established over a certain region. Derive an equation, in terms of the electric and magnetic field strength, for the speed of an electron traveling through the crossed-fields without deflection.
Use Maxwell's Equations to derive a decoupled set of wave equations for electric and magnetic fields in a linear, homogeneous, isotropic media characterized by (µ, ε, σ) in the absence of sources. Then modify these equations to describe waves propagating in free space. Show all work, please
4. Magnetic Dipole Moment on a PEC Sphere: In HW 4-Problem 5, you found the electric dipole moment for a metal sphere of radius a in a uniform electric field. In this problem you will find the magnetic dipole moment for the same metal sphere but now in a uniform magnetic field, Hext-Hext2. Note:Assume that the sphere is centered at the origin of a spherical coordinate system. Express Hext in spherical coordinates. To find the magnetic field that is induced...
B-Waves. Starting with Maxwell’s equations,
derive the 3-D wave equation for magnetic fields.
Gauss's law for electric fields Gauss's law for magnetic fields: Faraday's law: (11-31a) (11-31b) (11-31c) OE Ampere's law (11-31d)
Please help with the following problem
ctric dipole of co and directed along the x -axis. Derive the (a) far-zone fields radiated by the dipole (b) directivity of the antenna (c) determine polarization of the radiated far-zone fields (E ?,E ? ) in the following planes: (a) ? ?- (b) ?-90 (c) 0 90
1. Which statement about the nature of electric and magnetic fields is the most accurate? A)Fields can only ever be "electric" or "magnetic", regardless of reference frame. B)Whether a field is seen as "electric" or "magnetic" depends on the motion of the reference frame relative to the sources of the field. C)"Electric" and "magnetic" fields are entirely unrelated.