For a short dipole with length l such that l ≪ λ, instead of treating the current Ĩ(z) as...

For a short dipole with length l such that l ≪ λ, instead of treating the current Ĩ(z) as constant along the dipole, as was done in Section 9-1, a more realistic approximation that ensures the current goes to zero at the dipole ends is to describe Ĩ(z) by the triangular function

as shown in Fig. Use this current distribution to determine the following:

(a) The far-field Ẽ(R, θ, ϕ).

(b) The power density S(R, θ, ϕ).

(c) The directivity D.

(d) The radiation resistance Rrad.

Figure P: Triangular current distribution on a short dipole