Math 2105 PS 14
1. Evaluate ZZ
~ ⇥ (y~i) · ~n d
r
S
where S is the hemisphere x + y 2 + z 2 = 1,
2
z 0.
x̅
Ex y j z
E
0 0
y
f Yz y 72 1 0
Î 22k
2 2yj
5 2 1 29J 22
TL4127
yn
Therefore
Fx y w̅ E x tyj zI z
f
d DA da
1,27,72 7
1 Eddy
TE
, have
plug them nto the ntegral
we
If we
zl.IE da
f Fxly l. dr
ffl
R s the
y
d sk
1 coord.fr
f dxdy
2M 1
we can use polar
f
rose drdo
yers n
r 1 00AM
1 do
do
2M
M
i i
1. Evaluate ZZ
~ ⇥ (y~i) · ~n d
r
S
where S is the hemisphere x + y 2 + z 2 = 1,
2
z 0.
x̅
Ex y j z
E
0 0
y
f Yz y 72 1 0
Î 22k
2 2yj
5 2 1 29J 22
TL4127
yn
Therefore
Fx y w̅ E x tyj zI z
f
d DA da
1,27,72 7
1 Eddy
TE
, have
plug them nto the ntegral
we
If we
zl.IE da
f Fxly l. dr
ffl
R s the
y
d sk
1 coord.fr
f dxdy
2M 1
we can use polar
f
rose drdo
yers n
r 1 00AM
1 do
do
2M
M
i i
