Only 4.10 (b) using the vector potential approach... Thank you!
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Only 4.10 (b) using the vector potential approach... Thank
you!
14.9. An infinitesimal magnetic dipole of...
1. 135 points] A horizontal infinitesimal electric dipole of a constant current I, has the length,...
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.
Problem 2 An infinitesimal electric dipole is centered at the origin and lies on the x-y...
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.
Using the vector potential A and the procedure outlined in Section 3.6 of Chapter 3, derive...
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...
Please help with the following problem ctric dipole of co and directed along the x -axis....
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
The approximate far zone normalized electric field radiated by a resonant linear dipole antenna used in wireless mobile...
The approximate far zone normalized electric field radiated by a resonant linear dipole antenna used in wireless mobile units, positioned symmetrically at the origin along the z- axis, is given by 0°0 180° 1.5 ejkr EaâgEa sin 0° e 360° where E is a constant and r is the spherical radial distance measured from the origin of the coordinate system. Determine the: (a) Exact maximum directivity (dimensionless and in dB) (b) Half-power beamwidth (in degrees) (c) Approximate maximum directivity (dimensionless...
A very small circular loop of radius a(a < λ/6π) and constant current 10 is symmetrically placed ...
A very small circular loop of radius a(a < λ/6π) and constant current 10 is symmetrically placed about the originatO and with the plane of its area parallel to the y-z plane. Find the (a) spherical E- and H-field components radiated by the loop in the far zone (b) directivity of the antenna
A very small circular loop of radius a(a
1) A Hertzian dipole antenna is a short conducting wire carrying an approximately constant current over its length...
1) A Hertzian dipole antenna is a short conducting wire carrying an approximately constant current over its length If such a dipole is placed along the z-axis with its midpoint at the origin, and if the current flowing through it is i(t) ż lo cosot, assume I to be sufficiently small so that the observation point is approximately equidistant to all points on the dipole; that is, assume RR then the corresponding magnetic field is described by: olk2 sin e...
2. RFID Tag Magnetic field: Consider a square loop of wire that lies in the x-y plane and carries...
2. RFID Tag Magnetic field: Consider a square loop of wire that lies in the x-y plane and carries an electric current lo. The center of the loop is located at the origin and each side has length a. The current flows in a counter-clockwise direction as shown in the figure below Note*: This is a common design for an RFID tag's antenna, we will analyze RFID tag detection at a later time. a) Using Biot-Savart's law, find an expression...
normal 2. RFID Tag Magnetic field: Consider a square loop of wire that lies in the...
normal 2. RFID Tag Magnetic field: Consider a square loop of wire that lies in the x-y plane and carries an electric current lo. The center of the loop is located at the origin and each side has length a. The current flows in a counter-clockwise direction as shown in the figure below. Note*: This is a common design for an RFID tag's antenna, we will analyze RFID tag detection at a later time. Using Biot-Savart's law, find an expression...
Consider a cylindrical capacitor like that shown in Fig. 24.6. Let d = rb − ra...
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...
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.
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.
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...
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
The approximate far zone normalized electric field radiated by a resonant linear dipole antenna used in wireless mobile units, positioned symmetrically at the origin along the z- axis, is given by 0°0 180° 1.5 ejkr EaâgEa sin 0° e 360° where E is a constant and r is the spherical radial distance measured from the origin of the coordinate system. Determine the: (a) Exact maximum directivity (dimensionless and in dB) (b) Half-power beamwidth (in degrees) (c) Approximate maximum directivity (dimensionless...
A very small circular loop of radius a(a < λ/6π) and constant current 10 is symmetrically placed about the originatO and with the plane of its area parallel to the y-z plane. Find the (a) spherical E- and H-field components radiated by the loop in the far zone (b) directivity of the antenna
A very small circular loop of radius a(a
1) A Hertzian dipole antenna is a short conducting wire carrying an approximately constant current over its length If such a dipole is placed along the z-axis with its midpoint at the origin, and if the current flowing through it is i(t) ż lo cosot, assume I to be sufficiently small so that the observation point is approximately equidistant to all points on the dipole; that is, assume RR then the corresponding magnetic field is described by: olk2 sin e...
2. RFID Tag Magnetic field: Consider a square loop of wire that lies in the x-y plane and carries an electric current lo. The center of the loop is located at the origin and each side has length a. The current flows in a counter-clockwise direction as shown in the figure below Note*: This is a common design for an RFID tag's antenna, we will analyze RFID tag detection at a later time. a) Using Biot-Savart's law, find an expression...
normal 2. RFID Tag Magnetic field: Consider a square loop of wire that lies in the x-y plane and carries an electric current lo. The center of the loop is located at the origin and each side has length a. The current flows in a counter-clockwise direction as shown in the figure below. Note*: This is a common design for an RFID tag's antenna, we will analyze RFID tag detection at a later time. Using Biot-Savart's law, find an expression...
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...
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