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Problem 3. An electric dipole of magnitude Po is placed at the origin and rotates clockwise...
Consider a charge, q, rotating about the origin in the x–y plane at a radius, a, with angular frequency ω. Find the electric dipole, electric quadrupole, and magnetic dipole vector potentials in the radiation zone for this charge distribution. Please to show all of your step, thank!
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.
4. Magnetic dipole radiation- two loops
Consider a circular current loop in the xy plane of radius b as
in Section 11.1.3(See image above). Suppose there is another
parallel identical loop placed a distance d above the first loop.
The directions of the currents in the two loops are both
counterclockwise. The long wavelength approximation is
applicable.
(a) Compute the total vector potential A at positions in the
radiation zone.
(b) Compute the total magnetic field in the radiation zone....
A wire dipole of length λ/100 is placed at the origin, and aligned with the z axis. The current on the dipole may be assumed to be constant of value of 4. Drive and show the procedure to calculate the far-field electric and magnetic fields.
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
A particle is to move in an xy plane,
clockwise around the origin as seen from the positive side of the z
axis. In unit-vector notation, what torque acts on the particle at
time t = 9.1 s if the magnitude of its angular momentum about the
origin is (a)3.2 kg·m2/s, (b)3.2t2 kg·m2/s3, (c)3.2t1/2 kg·m2/s3/2,
and (d)3.2/t2 kg·m2*s?
A particle is to move in an xy plane, clockwise around the origin as seen from the positive side of the z axis. In unit-vector notation, what torque acts on the particle at time t = 8.6 s if the magnitude of its angular momentum about the origin is (a)7.0 kg·m2/s, (b)7.0t2 kg·m2/s3, (c)7.0t1/2 kg·m2/s3/2, and (d)7.0/t2 kg·m2*s?
A magnetic dipole m(t) = m_0*cos(ωt) can be described as current density j(r,t) = −cm(t) × ∇δ(r) at it's origin. Calculate (a) the retarded potentials Φ(r,t) and A(r,t) (b) the electric/magnetic fields E and B as well as their simplifications for far and near field (c) the Poynting vector S in far field as well as the whole emitted power
A magnetic dipole m(t) = m_0*cos(ωt) can be described as current density j(r,t) = −cm(t) × ∇δ(r) at it's origin. Calculate (a) the retarded potentials Φ(r,t) and A(r,t) (b) the electric/magnetic fields E and B as well as their simplifications for far and near field (c) the Poynting vector S in far field as well as the whole emitted power