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The
x
and the y components are
2
1
sin
4
x
dx
dE
r
θ
ε
0
λ
=−
π
and
2
1
cos
4
y
dx
dE
r
0
λ
π
,
respectively. We use
as the variable of integration and substitute
r
=
R
/cos
,
tan
xR
=
and
dx
=
(
R
/cos
2
)
d
. The limits of integration are 0 and
π
/2 rad. Thus,
0
0
00
0
sin
cos
44
4
x
Ed
R
RR
θθ
εε
π2
λλ
λ
=
ππ
π
∫
and
/2
0
0
0
cos
sin
.
4
y
R
π
λ
π
∫
We notice that
E
x
=
E
y
no matter what the value of
R
. Thus,
G
E
makes an angle of 45°
with the rod for all values of
R
.
33. Consider an infinitesimal section of the rod of length
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This note was uploaded on 06/07/2010 for the course PHYS 344 taught by Professor Bb during the Spring '10 term at The Petroleum Institute.
 Spring '10
 BB
 Physics, Charge

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