082-Engineering-Mathematics-Anthony-Croft-Robert-Davison-Martin-Hargreaves-James-Flint-Edisi-5-2017

Review exercises 4 173
z
z
Feeding lines
attached to
an a.c source
f
Antenna
elements
3D radiation
pattern
Figure4.29
The half-wave dipole antenna and itsradiation pattern in sphericalpolar coordinates.
EXERCISES4.7
1 Apoint has spherical polar coordinates (3,40 ◦ ,70 ◦ ).
Determine the Cartesian coordinates.
2 Apoint has Cartesian coordinates (1,2,3).Determine
the spherical polar coordinates.
3 Describe the surfaceR = 1,0 ◦ θ 360 ◦ ,
0 ◦ φ90 ◦ .
Solutions
1 (2.1595,1.8121, 1.0261)
3 A hemisphere ofradius1. Theflat sideis onthex--y
2 R = 3.7417, θ = 63.43 ◦ , φ = 36.70 ◦ plane.
TechnicalComputingExercises4.7
Useatechnical computing language such as
MATLAB ® to produce a plotsimilarto Engineering
application 4.3. You may findithelpful to firstgenerate
asetofnumbers0 t < 2π andthen use a builtin
functionsuch aspolarorpolarplotto generate a
graphofthe equation.
REVIEWEXERCISES4
1 Phas Cartesian coordinates (6, −3, −2).Calculate
the distance ofPfrom the origin.
2 Phas Cartesian coordinates (−4, −3).Calculate the
polar coordinates ofP.
3 Phas polar coordinates (5,240 ◦ ).Calculate the
Cartesiancoordinates ofP.
4 Describe the surface defined by
1r4,0 ◦ θ90 ◦ .
5 Calculate the cylindrical polar coordinates ofapoint
with Cartesian coordinates (−1,4,1).
6 Describe the surfacex = 0 in three dimensions.