Ch. 16, problem 1: Find the total positive charge of all the protons in 1.0 mol of water.
[number of protons in a molecule] = nmolec
=
[number of molecules in a mole] = 6.02 ×10 [amount of charge per proton ] = 1.602 ×10 p +
N ⋅ e = nmolec N A ⋅ e = (10 molec )(6.02 ×10
→
Q = nmolesQɶ = (1.00 mol) × (9.64 ×10
5 C mol
2 nH +1nO 23 molec = mol
19 C = p +
−
23 molec mol
=
N A
p + = molec
(2 + 8) =
10
p+ molec
;
[Avogadro's number ];
e;
)(1.602 ×10
19 C p +
−
) = 9.64 ×10
5
) = 9.64 ×10 C
5
C = mol
Qɶ
balloon, initially neutral, neutral, is rubbed rubbed with with fur until it acquires acquires a net charge charge of −0.60 nC. nC. Ch. 16, problem 3: A 3: A balloon, (a) Assuming that only electrons are transferred, were electrons removed from the balloon or added to it? Added; for the balloon to acquire a negative charge, negatively-charged species must be added to it. (b) How many electrons were transferred?
q = Ne → N
=
q e
0.60 ×10 9 C −
− =
19 C e−
−
1.602 ×10
−
=
9
3.7 ×10 e −
positively charged charged rod is is brought brought near two two uncharged uncharged conducting conducting spheres spheres of the the same Ch. 16, problem 5: A positively size that are initially touching each other (diagram a). The spheres are moved apart and then the charged rod is removed (diagram b),
(a)
; (b)
(a) What is the sign of the net charge on sphere 1 in diagram b? Negative; in configuration-a, the rod initially draws out negative charge. (b) In comparison with the charge on sphere 1, how much and what sign of charge is on sphere 2? Because the system must stay charge-neutral, sphere-2 must gain an opposite charge of sphere-1; namely, positive. Summarily, the spheres bear equal and opposite charges. N.B., this is an example of a dipole; an electrical configuration that proliferates in nature. Side discussion on dipoles: a point-charge = a monopole. Net charge of a monopole is, say, -0.6 nC (e.g.,
balloon, above). The force exerted between monopoles is F
=
k
q1q2 2
r
, which looks a lot like the gravitational-law
studied last semester (not a coincidence). Example of monopoles in nature: charged balloon, you scuff your feet on the carpet and touch a doorknob on a dry day, van der Graff generators, possibly the lightning-bolt sphere out in the lobby. An electric monopole is unstable; usually, as soon as something gains a net charge, nature works to relax it. For instance, you can’t really get that doorknob shock on a humid day; the water droplets in humid air act to carry away the net charge. Net charge of a dipole is ZERO. Force exerted between dipoles is…complicated, and won’t be addressed in this course. Examples of dipoles in nature: almost any molecule has either a temporary or permanent dipole (e.g., H2O, NH3 have permanent, and any other molecule has temporary, which is called London dispersion/van der Waals forces), any object near a monopole, any object near a dipole. An electric dipole is also unstable, but it happens very easily by small fluctuations in charge configuration; due to atomic motion, billions upon billions of little dipoles are created or destroyed by the 10 -12 second in any solid, liquid, or gas. E.g., dipoles are almost impossible to avoid, merely by virtue of a presumably-spherical charged species (e.g., electron, proton) having a finite radius.
Ch. 16, problem 9: If the electric force of repulsion between two 1-C charges is 10 N, how far apart are they? F
=
k
q1q2 r
2
r
↔
=
kq1q2
2
9
=
m (9 × 10 N C 2 )(1 C)(1 C)
10 N
F
=
3 × 104 m = 30 km = 18.6 miles
Ch. 16, problem 10: Two small metal spheres are 25.0 cm apart. The spheres have equal amounts of negative charge and repel each other with a force of 0.036 N. What is the charge on each sphere? F
=
kq1q2 r
2
q1 = q2 = q
=
kq 2 r
2
↔
q=
Fr 2
(0.036 N)(0.25 m) 2
=
9
k
m2 2 C
(9 × 10 N )
=
5 × 10 7 C −
Ch. 16, problem 13: A + 2.0-nC point charge is 3.0 cm away from a -3.0-nC point charge. (a) What are the magnitude and direction of the electric force acting on the + 2.0-nC charge? Coulomb’s Law tells you the relative force between them, F
=
k
q1q2 r2
m 2 (2.0 ×10 9 C )(−3.0 × 10 9 C ) ) = (9 × 10 N = (0.03 m) 2 C 2 −
9
−
−
6 × 10 5 N −
=
an attractive force along the line between charges
Negative sign indicates attractive force. Positive sign indicates repelling-force. As for absolute force between then, you will need to define a coordinate system. (b) What are the magnitude and direction of the electric force acting on the -3.0-nC charge? Short answer: equal but opposite force.
