Convert unit vector from cartesian to spherical coordination

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SUMMARY

The discussion focuses on converting unit vectors from Cartesian coordinates (x^, y^, z^) to spherical coordinates (r^, θ^, ∅^). The user seeks clarification on how the transformation of the unit vector (-x^) to (∅^.sinθ) is achieved. The solution involves understanding the relationships between these coordinate systems, specifically the mathematical formulas for conversion. The correct terminology for the coordinate systems is emphasized as 'Cartesian coordinates' and 'spherical coordinates'.

PREREQUISITES
  • Understanding of Cartesian coordinates
  • Familiarity with spherical coordinates
  • Basic knowledge of vector notation
  • Mathematical skills for coordinate transformation
NEXT STEPS
  • Study the mathematical formulas for converting between Cartesian and spherical coordinates
  • Learn about vector transformations in physics
  • Explore the concept of unit vectors in different coordinate systems
  • Review applications of spherical coordinates in electromagnetic theory
USEFUL FOR

Students and professionals in physics, electrical engineering, and mathematics who need to understand coordinate transformations and their applications in fields such as antenna theory and wave propagation.

assassin2811
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i have a problem :
A small loop antenna in free space and centered about the origin on the xy-plane is producing a
(far-field) radiation electric field (in phasor notation) :
http://postimg.org/image/63tm76h5l/

and their solution :
http://postimg.org/image/6mdm6roh9/

i don't understand how can they replace (-x^) with (∅^.sinθ), can anyone show me how to convert unit vectors in cartesian coordination (x^, y^, z^) into spherical (r^, θ^, ∅^), thanks
 
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