Electric Charges problem answers for #2, 8 and 17 and questions 3,6 and 10
2.Use the charge per electron to find the number of electrons.
æ
ö
1electron
(- 48.0 ´ 10-6 C) ç
= 2.996 ´ 1014 electrons » 3.00 ´ 1014 electrons
-19 ÷
è -1.602 ´ 10 C ø
8.Use the charge per electron and the mass per electron.
æ
ö
1electron
(-28 ´ 10-6 C) ç
= 1.748 ´ 1014 » 1.7 ´ 1014 electrons
-19 ÷
è -1.602 ´ 10 C ø
æ 9.109 ´ 10-31 kg ö
-16
-16
(1.748 ´ 1014 e- ) ç
÷ = 1.592 ´ 10 kg » 1.6 ´ 10 kg
1e
è
ø
17.(a) If the force is repulsive, then both charges must be positive since the total charge is positive. Call
the total charge Q.
Q1 + Q2 = Q
Q1 =
F=
Q ± Q2 - 4
kQ1Q2
d2
=
kQ1(Q - Q1 )
d2
® Q12 - QQ1 +
Fd 2
=0
k
Fd 2
k
2
é
(12.0 N)(0.280 m)2 ùú
= 12 ê(90.0 ´ 10-6 C) ± (90.0 ´ 10-6 C)2 - 4
ê
(8.988 ´ 109 N × m 2 /C2 ) úû
ë
= 88.8 ´ 10-6 C, 1.2 ´ 10-6 C
(b)
If the force is attractive, then the charges are of opposite sign. The value used for F must then
be negative. Other than that, the solution method is the same as for part (a).
Q1 =
Q ± Q2 - 4
Fd 2
k
2
é
(-12.0 N)(0.280 m)2 ùú
= 12 ê(90.0 ´ 10-6 C) ± (90.0 ´ 10-6 C)2 - 4
ê
(8.988 ´ 109 N × m 2 /C2 ) úû
ë
= 91.1 ´ 10-6 C, - 1.1 ´ 10-6 C
3.Fog or rain droplets tend to form around ions because water is a polar molecule (Fig. 16–4), with a
positive region and a negative region. The charge centers on the water molecule will be attracted to
the ions or electrons in the air.
6.The net charge on a conductor is the sum of all of the positive and negative charges in the conductor. If a
neutral conductor has extra electrons added to it, then the net charge is negative. If a neutral
conductor has electrons removed from it, then the net charge is positive. If a neutral conductor has
the same amount of positive and negative charge, then the net charge is zero.
The “free charges” in a conductor are electrons that can move about freely within
the material because they are only loosely bound to their atoms. The “free electrons”
are also referred to as “conduction electrons.” A conductor may have a zero net
charge but still have substantial free charges
10.Coulomb’s law and Newton’s law are very similar in form. When expressed in SI units, the magnitude
of the constant in Newton’s law is very small, while the magnitude of the constant in Coulomb’s
law is quite large. Newton’s law says the gravitational force is proportional to the product of the
two masses, while Coulomb’s law says the electrical force is proportional to the product of the two
charges. Newton’s law produces only attractive forces, since there is only one kind of gravitational
mass. Coulomb’s law produces both attractive and repulsive forces, since there are two kinds of
electrical charge.