Antennas

Problem:

Consider a linear antenna of length d (d << λ) with a narrow gap in the center for the purposes of excitation.  Assume that the current is sinusoidal and in the same direction in each half of the antenna, having a value of I0 at the gap and falling linearly to zero at the ends.  Find the power radiated in the electric dipole approximation.

Solution:

Problem:

Assume an antenna is aligned with the z-axis and extends from z = -λ/4 to z = +λ/4.  Assume the current in the antenna varies as I(z,t) = I0sin(ωt)cos(kz).  Calculate the radiation fields ER and BR and the average Poynting vector.

Solution:

Problem:

A very thin, straight, conducting wire is centered on the origin of coordinates and is oriented along the z-axis.  The wire carries a current I = I0cos(ω0t) everywhere along its length l.
(a)  Obtain the vector potential everywhere outside the source region for distances r >> l.  Hint: Use the Lorentz gauge.  Make no assumption about the value of the wavelength, λ0 = 2πc/ω0.
(b)  Obtain the dependence of the intensity of the radiation pattern emitted by the wire on the angle θ in the regime  r >> l >> λ0.

Solution: