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Physics 2212 GPS Week 14
Problem #
A cube of size d is centered at the origin. There is a
non-constant electric field everywhere in space given as:
ω E(x, y, z) =< e
x
, → 10 y, z
3
>
The electric field, for example, on the right-side face of
the box at location < d/ 2 , 0 , 0 > is
ω E =< e
d/ 2
, 0 , 0 >.
A. Calculate the electric flux on the right-side face of the box. Show your work.
B. Calculate the electric flux on the left-side face of the box. Show your work.
C. Calculate the electric flux on the top face of the box. Show your work.
min
I
26
,
E
= se"
,
loy
,
23
t
= e
d
b
h
i =
,
1
,
E
=
< e"
,
log
,
23
En
=
-log
=
d
=
D. Calculate the electric flux on the bottom face of the box. Show your work.
E. Calculate the electric flux on the front face of the box. Show your work.
F. Calculate the electric flux on the back face of the box. Show your work.
G. What is the total electric flux through this box-shaped surface?
E
.
2
20
,
10
gi
>.
,
,
>
p
=
E = sc *, Toy ,
23
1 =
1 0
,
0
1
0
:
(t =
=
d
E
n
=
,
,
↑
= -7)
:
d
Profal
=
E
C. Use Gauss’s law to calculate the electric field within the shell itself (that is, for R < r < 2 R) as a function
of r.
D. Use Gauss’s law to calculate the electric field outside the shell’s outer radius (that is, for r > 2 R) as a
function of r.
Qe
P(Ur-VR)
·
Qu
Mi
E
=
Q
A
: Tor
Fir-Yark
?
)
do(Yir")
·
