Campos
CartesianCoordinates(x, y, z)
af. af Vf = - , + O i, + af i,
ax ay
Oz
aA, aA, + aA, V . A= a+
ax ay az
(LAX,
A
AaA\
.a,
Ox
OA. a
ay z
V2f a' +f + a'f az Ox jy
az
ax
ay
CylindricalCoordinates (r, 4, z)
Vf = arr
Of. I •af4 + af. 1 r04 az1a
rr
V *A=- -(rAr)+M +M
iA, 1
aA,
Oz
DA A. A, 1xzaz
rr a
I a BA, rr) r
aA.
'L
I(rAs)
ar
A
a4J
V~ f
la0
rr
-- r-
af\
-2 Ora r) 14 az
+
1 82f
a2f
SphericalCoordinates (r, 0,
4)
1 af.
If-14
a.
Vf=
af.
r
ar
,+
•O
ae+I
r sin 0 aO
A 1 (r 1 a(sin OAo) 1 oA* V" -A = (rPA,)+ + r ar r sin 0 ae r sin 0 a4 x 1 rsin a(sin OAs) aA]
a80
MA,
a 04,
a(rA,)) 1 [ra(rAo) dA,1 rr O OI a•f
S 1 r sio V'f =
arsin
r-r a-"
r+
a+sin 0 O+
Cartesian x y z
= =
=
Cylindrical
r cosc r sinq
z
Spherical
= =
=
r sin 0 cos 4 r sin 0 sin 4
r os 0
=
1
cos
i, - sin 0i
=
sin 0 cos
i, + cos 0 cos
4ie
-sin Ois
,Y
=
=
sin 0i, + cos 0ik
iz
= sin 0 sin 4i, +cos 0 sin
/ie
+ cos 46 i
= cos Oi,- sin Oie
Cylindrical
Cartesian
=r =
-=
Spherical
sin 0
tan- 1y/x
z
Sr
cos 0
=
=
=
cos kix, +sin
i,
= = =
sin Oi, +cos
ie
-sin 0ix +cos 4iy
i
i4 cos Oi, -sin 0iO
Spherical r
0
= cos
Cartesian
/x 2+y2+z
=
Cylindrical If,- ý+z
-1 z
cos
/x2'+y2+z'
2
= i, is i, = = =
cot- x/y sin 0cos ,ix +sin 0 sin (i, + cos Oi. cos 0 cos oi, +cos 0 sin -sin Oi. -sin 46i, +cos = sin Oi,+cos Oi, cos Oi, -sin
i4,
4i, =
=
Oi,
di,
Geometric relations between coordinates and unit vectors for Cartesian, cylir drical, and spherical coordinate systems.
ELECTROMAGNETIC FIELD THEORY:
a problem solving approach
MARKUS W H N Massachusetts Institute of Technology
to mypnrents
Preface
V
PREFACE Electromagnetic field theory is often the least popular course in the electrical engineering curriculum. Heavy reliance on vector and integral calculus can obscure physical phenomena so that the student becomes bogged down in the mathematics and loses sight of the applications. This book instills problem solving confidence by teaching through the use of a largenumber of worked examples. To keep the subject exciting, many of these problems are based on physical processes, devices, and models. This text is an introductory treatment on the junior level for a two-semester electrical engineering course starting from the Coulomb-Lorentz force law on a point charge. The theory is extended by the continuous superposition of solutions from previously developedsimpler problems leading to the general integral and differential field laws. Often the same problem is solved by different methods so that the advantages and limitations of each approach becomes clear. Sample problems and their solutions are presented for each new concept with great emphasis placed on classical models of such physical phenomena as polarization, conduction, and magnetization. A largevariety of related problems that reinforce the text material are included at the end of each chapter for exercise and homework. It is expected that students have had elementary courses in calculus that allow them to easily differentiate and integrate simple functions. The text tries to keep the mathematical development rigorous but simple by typically describing systems with linear, constant...
Regístrate para leer el documento completo.