harvey (zmh93) – Homework 1 – Hoffmann – (56745)
1
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001
10.0 points
There are two identical small metal spheres
with charges 27
.
5
μ
C and
−
19
.
119
μ
C.
The
distance between them is 8 cm. The spheres
are placed in contact then set at their original
distance.
Calculate
the
magnitude
of
the
force
between
the
two
spheres
at
the
final
position.
The
Coulomb
constant
is
8
.
98755
×
10
9
N
·
m
2
/
C
2
.
Correct answer: 24
.
6602 N.
Explanation:
Let :
q
A
= 27
.
5
μ
C
= 2
.
75
×
10
−
5
C
,
q
B
=
−
19
.
119
μ
C
=
−
1
.
9119
×
10
−
5
C
,
and
d
= 8 cm = 0
.
08 m
.
When
the
spheres
are
in
contact,
the
charges will rearrange themselves until equi
librium is reached. Each sphere will then have
half of the original total charge:
q
=
q
A
+
q
B
2
=
2
.
75
×
10
−
5
C
−
1
.
9119
×
10
−
5
C
2
= 4
.
19051
×
10
−
6
C
.
The force between the two spheres is
F
=
k
q
2
d
2
=
(
8
.
98755
×
10
9
N
·
m
2
/
C
2
)
×
(4
.
19051
×
10
−
6
C)
2
(0
.
08 m)
2
=
24
.
6602 N
.
002
10.0 points
Charge
Q
is on the
y
axis a distance
a
from
the origin and charge
q
is on the
x
axis a
distance
d
from the origin.
What is the value of
d
for which the
x
component of the force on
q
is the greatest?
1.
d
=
q
Q
a
2.
d
=
a
√
2
correct
3.
d
=
a
2
4.
d
=
q
Q
a
√
2
5.
d
=
q
Q
√
2
a
6.
d
=
√
2
a
7.
d
=
q
Q
a
2
8.
d
=
a
9.
d
= 0
Explanation:
We have the force on charge
q
on the
x
axis
due to charge
Q
on the
y
axis
vector
F
=
1
4
π ǫ
0
q Q
r
2
ˆ
r ,
where
r
=
radicalbig
a
2
+
d
2
. So the
x
component of
the force on
q
is
F
x
=
1
4
π ǫ
0
q Q
r
2
cos
θ
=
1
4
π ǫ
0
q Q
a
2
+
d
2
d
√
a
2
+
d
2
=
1
4
π ǫ
0
q Q d
(
a
2
+
d
2
)
3
/
2
.
For maximum
x
component
of the
force,
∂ F
x
∂d
= 0 is required. Therefore
∂F
x
∂d
=
q Q
4
π ǫ
0
a
2
−
2
d
2
(
a
2
+
d
2
)
5
/
2
= 0
a
2
−
2
d
2
= 0
d
=
a
√
2
.
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harvey (zmh93) – Homework 1 – Hoffmann – (56745)
2
003
(part 1 of 2) 10.0 points
A strong lightning bolt transfers
about
23
.
93 C to Earth.
How many electrons are transferred?
The
charge on an electron is
−
1
.
60218
×
10
−
19
C.
Correct answer: 1
.
49359
×
10
20
.
Explanation:
Let :
q
= 23
.
93 C
and
q
e
=
−
1
.
60218
×
10
−
19
C
.
The charge is proportional to the number
of electrons, so
q
=
n

q
e

n
=
q

q
e

=
23
.
93 C
−
1
.
60218
×
10
−
19
C

=
1
.
49359
×
10
20
.
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 Fall '08
 Turner
 Physics, Charge, Work, Correct Answer, Electric charge, Harvey

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