(a) Assume the spatial distribution of the current on a very thin centerfed half-wave dipole lying along the z-axis to be { I }_{ 0 }\cos { 2\pi z } . Find the charge distribution on the dipole. What is the wavelength? (b) Repeat part (a), assuming the current distribution along the dipole to be a triangular function described by
I\left( z \right) ={ I }_{ 0 }\left( 1-4\left| Z \right| \right)Question : (a) Assume the spatial distribution of the current on a very...
Equation of continuity: \overline { \nabla } .\overline { J } =-j\omega \rho
\rightarrow { \rho }_{ \ell }=\frac { j }{ \omega } =\frac { dI\left( z \right) }{ dz }
(a) I\left( z \right) ={ I }_{ 0 }\cos { 2\pi z } \rightarrow \rightarrow { \rho }_{ \ell }=-\frac { { I }_{ 0 } }{ c } \sin { 2\pi z }
\quad \quad \beta =\frac { 2\pi }{ \lambda } =2\pi
\rightarrow Wavelength\lambda =1\left( m \right)
I\left( z \right) ={ I }_{ 0 }\left( 1-\frac { 4 }{ \lambda } \left| z \right| \right) \rightarrow { \rho }_{ \ell }=[\begin{matrix} -j\frac { 2{ I }_{ 0 } }{ \pi c } forz>0 \\ +j\frac { 2{ I }_{ 0 } }{ \pi c } forz<0 \end{matrix}