전자기학 1

소개글

전자기학 1에 대한 보고서 자료입니다.

목차

1.1 Scalar and Vector

1.2 Cartesian Coordinate System
(a) Vector components and unit vectors
(b) Dot product
(c) Cross product
(d) Length, area, and volume
(e) Vector differentiation
- gradient
- divergence
- curl
(f) Vector identities (Appendix A.3)

1.3 Cylindrical Coordinate System

1.4 Spherical Coordinate System

본문내용

} hat a_z
(e2) Divergence of
vec A
The divergence of a vector is the limit of its surface integral per unit volume as the volume enclosed by the surface goes to zero, that is,
rm d i v it vec A ``=`` del cdot vec A ``=`` lim from{V 0} 1 over V int_s vec A cdot d vec s
The detail proof will be done later.(Gauss law)
Instead, from the definition of
del
,
del cdot vec A ``&=`` left( {partial} over {partial x} hat a_x `+` {partial} over {partial y} hat a_y `+` {partial} over {partial z} hat a_z `right) cdot left( A_x hat a_x `+` A_y hat a_y `+` A_z hat a_z `right) ## ``&=`` {partial A_x } over {partial x} `+` {partial A_y} over {partial y} `+` {partial A_z } over {partial z}
(e3) Curl of
vec A
The curl of a vector is the limit of the ratio of the integral of its cross product with the outward drawn normal, over a closed surface, to the volume enclosed by the surface as the
V `` `` 0
del times vec A ``=`` lim from{V 0} 1 over V OINT_s `` hat n times vec A cdot d vec s
The detail proof will be done later.(Stokes theorem)
Instead, from the definition of
del
,
del times vec A ``&=`` left( {partial} over {partial x} hat a_x + {partial} over {partial y} hat a_y + {partial} over {partial z} hat{a}_z `right) times left( A_x hat a_x `+` A_y hat a_y `+` A_z hat a_z `right) ## ``&=`` 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)
(f) Vector identities (Appendix A.3)
(vec A times vec B `) cdot vec C ``=``(vec B times vec C `) cdot vec A ``=`` (vec C times vec A `) cdot vec B
or
vec C cdot (vec A times vec B `) ``=`` vec A cdot (vec B times vec C `) ``=`` vec B cdot (vec C times vec A `)
vec A times ( vec B times vec C `) ``=`` vec B ` ( vec A cdot vec C `) `-` vec C `( vec A cdot vec B `) ``=`` ( vec A cdot vec C `) vec B `-` ( vec A cdot vec B `) vec C
del left( v `+` w `) ``=`` del v `+` del w
del cdot ` ( vec A `+` vec B `) ``=`` del cdot vec A `+` del cdot vec B
del times ( vec A `+` vec B `) ``=`` del times vec A `+` del times vec B
del(vw `) ``=`` v ` del w `+` w ` del v
del cdot (v vec A `) ``=`` v ` (del cdot vec A `) `+` del v cdot vec A
del times ( v vec A `) ``=`` v ` ( del times vec A `) `+` del v times vec A
del( vec A cdot vec B `) ``=`` ( vec A cdot del `) vec B `+` ( vec B cdot del `) vec A `+` vec A times ( del times vec B `) `+` vec B times ( del times vec A `)
del cdot ( vec A times vec B `) ``=`` vec B cdot ( del times vec A `) `-` vec A cdot ( del times vec B `)
del times ( vec A times vec B `) ``=`` vec A ( del cdot vec B `) `-` vec B ( del cdot vec A `) `+` ( vec B cdot del `) vec A `-` ( vec A cdot del `) vec B
del cdot del times vec A ``=`` 0
del times del v ``=`` 0
del cdot del v ``=`` del^2 v
del times del times vec A ``=`` del (del cdot vecA ) `-` del^2 vec A

키워드

전자기학,   Cartesian,   product,   vectors,   components,   gradient