전자기학 3

소개글

전자기학 3에 대한 보고서 자료입니다.

목차

1.4 Spherical Coordinate System

(a) Vector components and unit vectors

본문내용

partial x} over {partial theta} {partial} over {partial x} `+` {partial y} over {partial theta} {partial} over {partial y} `+` {partial z} over {partial theta} {partial} over {partial z} ## ``&=`` r `` cos theta `` cos phi `` {partial} over {partial x} `+` r `` cos theta `` cos phi `` {partial} over {partial y} `+` left( - r `` sin theta `right) `` {partial} over {partial z}
{partial} over {partial phi} ``&=`` {partial x} over {partial phi} {partial} over {partial x} `+` {partial y} over {partial phi} {partial} over {partial y} `+` {partial z} over {partial phi} {partial} over {partial z} ## ``&=`` - r `` sin theta `` sin phi {partial} over {partial x} `+` r `` sin theta `` cos phi `` {partial} over {partial y} `+` 0
{partial} over {partial x} ``=`` sin theta `` cos phi `` {partial} over {partial r} `+` 1 over r `` cos theta `` cos phi `` {partial} over {partial theta} `-` {sin phi} over {r ` sin theta} `` {partial} over {partial phi}
{partial} over {partial y} ``=`` sin theta `` sin phi `` {partial} over {partial r} `+` 1 over r cos theta `` sin phi `` {partial} over {partial theta} `-` {cos phi} over {r ` sin theta} {partial} over {partial phi}
{partial} over {partial z} ``=`` cos theta `` {partial} over {partial r} `-` {sin theta} over r `` {partial} over {partial theta}
(ex) Obtain
del cdot vec A
and
del times vec A
from the expressions in the
cartesian coordinate system.
del cdot vec A ``=`` {partial A_x } over {partial x} `+` {partial A_y} over {partial y} `+` {partial A_z } over {partial z}
del times vec A ``&=`` hat a_x `` left( {partial A_z} over {partial y} `-` {partial A_y} over {partial z} `right) `+` hat a_y `` left( {partial A_x} over {partial z} `-` {partial A_z} over {partial x} `right) ## &~~~`+` hat a_z `` left( {partial A_y} over {partial x} `-` {partial A_x } over {partial y} `right)
Use below relations !!!
{partial} over {partial x} ``=`` sin theta `` cos phi `` {partial} over {partial r} `+` 1 over r `` cos theta `` cos phi `` {partial} over {partial theta} `-` {sin phi} over {r ` sin theta} `` {partial} over {partial phi}
{partial} over {partial y} ``=`` sin theta `` sin phi `` {partial} over {partial r} `+` 1 over r cos theta `` sin phi `` {partial} over {partial theta} `-` {cos phi} over {r ` sin theta} {partial} over {partial phi}
{partial} over {partial z} ``=`` cos theta `` {partial} over {partial r} `-` {sin theta} over r `` {partial} over {partial theta}
BMATRIX { {A_r }## {A_theta }## {A_phi } ``} ``=`` BMATRIX { {sin theta `` cos phi}& {sin theta `` sin phi}& {cos theta }``## {cos theta ``cos phi}& { cos theta `` sin phi }& {-sin theta }`` ## {-sin phi }& {cos phi }& {0 } `` } BMATRIX { {A_x }## {A_y }## {A_z }``}
BMATRIX { {hata_r }## {hata_theta }## {hata_phi } ``} ``=`` BMATRIX { {sin theta `` cos phi}& {sin theta `` sin phi}& {cos theta }``## {cos theta ``cos phi}& { cos theta `` sin phi }& {-sin theta }`` ## {-sin phi }& {cos phi }& {0 } `` } BMATRIX { {hat a_x }## {hat a_y }## {hat a_z }``}

키워드

전자기학,   Vector,   components,   Coordinate,   Spherical,   matrix