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Physics 21 Spring 2008
February 10, 2008
Hour Exam I Review
Review I1.
••11. In Fig.
2124
, three charged particles lie on an
x
axis.
Particles 1 and 2 are fixed in place. Particle 3 is free to
move, but the net electrostatic force on it from particles 1
and 2 happens to be zero. If
, what is the ratio
?
Solution:
2111. With rightwards positive, the net force on
q
3
is
()
13
23
31
32
3
2
2
23
12
23
.
qq
FF F k
k
L
LL
=+=
+
+
We note that each term exhibits the proper sign (positive for rightward, negative for
leftward) for all possible signs of the charges. For example, the first term (the force
exerted on
q
3
by
q
1
) is negative if they are unlike charges, indicating that
q
3
is being
pulled toward
q
1
, and it is positive if they are like charges (so
q
3
would be repelled from
q
1
). Setting the net force equal to zero
L
23
=
L
12
and canceling
k
,
q
3
and
L
12
leads to
11
2
2
0
4.00.
4.00
q
q
+=
⇒
=
−
Review I2
••31.
Figure
2250
a
shows
a nonconducting rod with a
uniformly distributed
charge
+Q
. The rod forms a
halfcircle with radius
R
and produces an electric
field of magnitude
at
its center of curvature
P
. If
the arc is collapsed to a point at distance
R
from
P
(Fig.
2250
b
), by what factor is the
magnitude of the electric field at
P
multiplied?
Solution:
2231. First, we need a formula for the field due to the arc. We use the notation
λ
for the
charge density,
λ
=
Q
/L
.
Sample Problem 223 illustrates the simplest approach to
circular arc field problems. Following the steps leading to Eq. 2221, we see that the
general result (for arcs that subtend angle
θ
) is
[]
arc
00
2s
i
n
(/
2
)
sin( / 2)
sin(
/ 2)
44
E
rr
λ
λθ
θθ
πε
=−
−
=
.
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View Full DocumentNow, the arc length is
L = r
θ
if
is expressed in radians. Thus, using
R
instead of
r
, we
obtain
arc
2
00
0
2(
/ )sin( / 2)
2(
/
)sin( / 2)
2 sin( / 2)
44
4
QL
QR
Q
E
rr
R
θθ
π
επ
ε
==
=
.
The problem asks for the ratio
E
particle
/
E
arc
where
E
particle
is given by Eq. 223:
2
particle
0
2
arc
0
/4
2 sin( / 2) / 4
2sin( / 2)
E
EQ
R
πε
θπ
.
With
= π
, we have
particle
arc
1.57.
2
E
E
=≈
Review I3
••51.
In Fig.
2352
, a solid sphere of radius
is
concentric with a spherical conducting shell of inner radius
and outer radius
. The sphere has a net
uniform charge
; the shell has a net charge
. What is the magnitude of the electric field at
radial distances (a)
, (b)
, (c)
, (d)
, (e)
, and (f)
? What is the net
charge on the (g) inner and (h) outer surface of the shell?
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 Spring '08
 Kim
 Charge, Force

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