Electromagnetic-Theory-I-(Physics-3300A)- - - - - - - 2011 ...mgc/Formula-Sheet-Mid.pdf ·...
Transcript of Electromagnetic-Theory-I-(Physics-3300A)- - - - - - - 2011 ...mgc/Formula-Sheet-Mid.pdf ·...
Electromagnetic Theory I (Physics 3300A) 2011-‐2012 Formula Sheet (for Midterm 2)
(You will be provided with a copy of this Formula Sheet for the test. Do NOT bring your own copy) Section2
F =14!"0
qQre2 r̂e
E(r) = 1
4!"0#( !r )re2 r̂evolume" d !$
E !da
surface!" =1!0Qenc
!"E =1!0" E = !"V
!2V = "!"0
V (r) =14!"0
! #( "r )re
d "$
Eabove !Ebelow =1!0" n̂
W =
12
14!"0
qiqjreijj=1(i! j )
n
"i=1
n
"
W =12
qiV (ri )i=1
n
! !"E = 0
W =!02
E 2 d"allspace!
f = 1
2!0" 2 n̂
P = !0
2E 2
C = Q
V W =
12CV 2
W =12
!V d"!
Section 3
V (r) = 14!"0
1r ! #( "r )d "! +
1r2
"r cos ""! #( "r )d "! +1r3
( "r )2 32cos2 "" #
12
$
%&
'
()! #( "r )d "! +!
*
+,
-
./ p = qd
Vdip (r) =
14!"0
p ! r̂r2
Section 4 p =!E N = p!E F = p !"E ! b = P ! n̂ !b = !"#P D = !0E+P !"D = ! f
D !da =Qf "enc!# P = !0"eE D = !E ! = !r!0
!r =1+ "e V (r) = 1
4!"0r̂c !P( "r )rc2V# d "#
Section 5
F = Q[E+ (v!B)] Fmag = I (dl!B)" !" J = #$!
$t !"B = 0 !"B = µ0J
B !dl!" = µ0Ienc B(r) =
µ04!
I! r̂crc2" d #l =
µ04!
I d #l ! r̂crc2"
A(r) = µ0
4!J( !r )rc
" d !"
B = !"A !"A = 0 !2A = "µ0J Babove !Bbelow = µ0 (K" n̂)
A(r) = µ0I4!
1r2
!r cos !!!" d !l + 1r3
( !r )2 32cos2 !! #
12
$
%&
'
()!" d !l +!
*
+,
-
./
Adip (r) =µ0I4!
m! r̂r2
m = I da! = I a