From symmetry, we see that there is no net force in the vertical direction on
q
2
= –
e
sitting at a distance
R
to the left of the coordinate origin.
We note that the net
x
force
caused by
q
3
and
q
4
on the
y
axis will have a magnitude equal to
3
22
2
00
0
2c
o
s
o
s
o
s
44
(
/
c
o
s
)
4
qe
qe
qe
rR
R
θ
πε
==
.
Consequently, to achieve a zero net force along the
x
axis, the above expression must
equal the magnitude of the repulsive force exerted on
q
2
by
q
1
= –
e
. Thus,
32
3
o
s
2
c
o
s
qe
e
e
q
RR
π
επ
ε
=⇒
=
.
Below we plot
q/e
as a function of the angle (in degrees):
The graph suggests that
q/e
< 5 for
< 60º, roughly.
We can be more precise by solving
the above equation.
The requirement
that
q
≤
5
e
leads to
31
/
3
1
5c
o
s
2cos
(10)
e
e
≤⇒
≤
which yields
≤
62.34º.
The problem asks for “physically possible values,” and it is
reasonable to suppose that only positiveintegermultiple values of
e
are allowed for
q
.
If
we let
q
=
ne
, for
n
= 1 … 5, then
N
will be found by taking the inverse cosine of the
cube root of (1/2
n
).
34. Let
d
be the vertical distance from the coordinate origin to
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview. Sign up
to
access the rest of the document.
 Spring '08
 Any
 Physics, smallest value, coordinate origin

Click to edit the document details