PHY 132 Midterm 1
Feb 26, 2004
Version
A
Put FULL NAME, ID#, and EXAM VERSION on the front cover of the BLUE BOOKLET!
To avoid problems in grading: do all problems in order
, write legibly
, and show all work for partial credit
!
Note: make sketches where appropriate and show your axis conventions. Do not forget units, number of signifi
cant digits, and check your results for consistency. This exam will last 1.5 hr. Success!
1.
Two point charges are positioned as follows:
Q
1
= +3.6 μC at
x
= 8.0 cm, y =0.0 cm; and
Q
2
=
−
6.4 μC at
y
= 6.0 cm and
x
=0. Show all work!
(40 points)
a.
Calculate the components of the electric field
E
at point P (
x
=8.0 cm,
y
=6.0 cm).
Solution:
(9 points) In P, the
E
x
is given by
Q
2
, and the
E
y
by
Q
1
:
E
x
= 1/(4
πε
0
)
Q
2
/(8.0 cm)
2
= 9×10
9
× –6.4×10
–6
/
64×10
–4
= –9×10
6
N/C (
B
: 9×10
6
N/C)
E
y
= 1/(4
πε
0
)
Q
1
/(6.0 cm)
2
= 9×10
9
× 3.6×10
–6
/
36×10
–4
= 9×10
6
N/C
(
B
: –9×10
6
N/C)
b.
Calculate the electric potential energy of the system consisting of
Q
1
and
Q
2
.
Solution:
(11 points) The potential energy of the two charges
Q
1
and
Q
2
, with separation distance 10.0
cm, is simply
U
=
Q
1
V
Q
2
= 1/(4
πε
0
)
Q
1
Q
2
/(10.0 cm) = 9×10
9
×3.6×10
–6
×–6.4×10
–6
/10×10
–2
= –2.07 J
c.
Calculate the electric potential at point P
Solution:
(9 points) The potential in P is the
scalar
sum of the potentials in P of
Q
1
and
Q
2
:
V
=
V
Q
1
+
V
Q
2
= 1/(4
πε
0
) [
Q
1
/(6.0 cm) +
Q
2
/(8.0 cm)] = 9×10
9
×[6.0×10
–5
– 8.0×10
–5
] = –1.8×10
5
V (
B
:
+1.8×10
5
V)
d.
Calculate the electric force
F
(magnitude and direction) on a point charge
q
=
−
2.0 μC placed in point P.
Solution:
(11 points) In P, the
F
x
is given by
qE
x
and
F
y
by
qE
y
:
F
x
= –2.0×10
–6
/(4
πε
0
)
Q
2
/(8.0 cm)
2
= +18 N and
F
y
= –2.0×10
–6
/(4
πε
0
)
Q
1
/(6.0 cm)
2
= –18 N.
(
B
:
F
= (+36 N, –36 N)
Thus:
F
= 18
√
2 = 25.5 N (
B
: 50.9 N), direction: –45° down from the
x
axis.
2.
Consider two long conducting coaxial
cylinders
. The inner cylinder has a total linear charge density +
λ
, an
inner radius
a
, and an outer radius
b
. The outer conducting cylinder has a total linear charge density
−
λ
, an
inner radius
c
, and an outer radius
d
. Thus:
a<b<c<d
. Initially the space between the cylinders is filled with
air (
K
= 1.00).
(60 points)
a.
Calculate the electric field at
i
)
r<a
,
ii
)
a<r<b
,
iii
)
b<r<c
,
iv
)
c<r<d
, and
v
)
r>d
. Note that for proper
credit for your answers you
must
give valid arguments, derivations, or proofs!
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 Spring '04
 Rijssenbeek
 Physics, Charge, Electric Potential, Electrostatics, Work, Electric charge

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