20.1
ELECTRIC CHARGE, FORCE, AND FIELD
20
E
XERCISES
Section 20.1 Electric Charge
14.
Nearly all of the mass of an atom is in its nucleus, and about one half of the nuclear mass of the light elements in
living matter (H, O, N, and C) is protons. Thus, the number of protons in a 65 kg averagesized person is
approximately
27
28
1
2
(65 kg)/(1.67
10
kg)
2
10 ,
−
×
<
×
0
,
e
which is also the number of electrons, since an average
person is electrically neutral. If there were a charge imbalance of
a person’s net charge
would be about
or several coulombs (huge by ordinary standards).
9
proton
electron


1
q
q
−
−
=
28
9
19
2
10
10
1.6
10
C
3.2 C,
−
−
± ×
×
×
×
= ±
15.
I
NTERPRET
This problem deals with quantity of charge in a typical lightning flash. We want to express the
quantity in terms of elementary charge
e
.
D
EVELOP
Since the magnitude of elementary charge
e
is
the number of electrons involved is
given by
19
1.6
10
C,
e
−
=
×
/ .
Q e
E
VALUATE
Substituting the values given in the problem statement, we find the number to be
20
19
25 C
/
1.
1.6
10
C
N
Q e
−
=
=
=
×
×
56
10
A
SSESS
Since 1 coulomb is about
elementary charges, our result has the right order of magnitude.
18
6.25
10
×
16.
(a)
The proton’s charge is
2
2
1
3
3
3
1
corresponding to a combination of
uud
quarks;
(b)
for neutrons,
,
e
e
e
e
=
+
−
0
=
2
1
1
3
3
3
−
−
corresponds to
udd
. (See Chapter 39, or Chapter 45 in the extended version of the text.)
Section 20.2 Coulomb’s Law
17.
I
NTERPRET
In this problem we are asked to compare the gravitational and electrical forces between a proton and
an electron.
D
EVELOP
The gravitational force and the electrostatic force between a proton and an electron separated by a
distance
r
are, respectively,
grav
2
p
e
Gm m
F
r
=
and
2
elec
2
ke
F
r
=
E
VALUATE
The ratio of the two forces is
2
2
9
2
2
19
2
elec
2
11
2
2
27
grav
39
(9
10
N
m /C
)(1.6
10
C)
(6.67
10
N
m /kg
)(1.67
10
kg)(9.11
10
kg)
2.3
10
p
e
F
ke
r
F
Gm m
r
−
−
−
⎛
⎞
⎛
⎞
×
⋅
×
=
=
⎜
⎟
⎜
⎟
⎜
⎟
×
⋅
×
×
⎝
⎠
⎝
⎠
≈
×
31
−
Note that the spatial dependence of both forces is the same, and cancels out.
A
SSESS
At all distances (for which the particles can be regarded as classical point charges), the Coulomb force is
about
10
times stronger than the gravitational force.
40
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