Chapter 21: Coulomb’s Law

In an early model of the hydrogen atom (the Bohr model), the electron orbits the proton in uniformly circular motion.The radius of the circle is restricted (quantized) to certain values given by${\mathbf{\text{r=n}}}^{\mathbf{\text{2}}}{\mathbf{\text{a}}}_{\mathbf{\text{0}}}\mathbf{\text{,forn=1,2,3,}}$. . . ,where${\mathbf{\text{a}}}_{\mathbf{\text{0}}}\mathbf{\text{=52.92pm}}$.What is the speed of the electron if it orbits in

(a) the smallest allowed orbit and (b) the second smallest orbit? (c)

If the electron moves to larger orbits, does its speed increase, decrease,

or stay the same?

A$\mathbf{\text{100W}}$lamp has a steady current of$\mathbf{\text{0.83A}}$in its filament. How long is required for$\mathbf{\text{1mol}}$of electrons to pass through the lamp?

The charges of an electron and a positron are $\mathbf{\text{-eand+e}}$. The mass of each is$\mathbf{9}\mathbf{.11}\mathbf{}\mathbf{\times }\mathbf{}{\mathbf{10}}^{\mathbf{-}\mathbf{31}}\mathbf{}\mathbf{\text{\hspace{0.17em}kg}}$.What is the ratio of the electrical force to the gravitational force between an electron and a positron?

In Fig. 21-23, three charged particles lie on an x-axis. Particles 1 and 2 are fixed in place. Particle 3 is free to move, but the net electrostatic force on it from particles 1 and 2 happens to be zero. If ${\mathbf{L}}_{\mathbf{23}}\mathbf{=}\mathbf{}{\mathbf{L}}_{\mathbf{12}}$, what is the ratio ${\mathbf{q}}_{\mathbf{1}}\mathbf{/}{\mathbf{q}}_{\mathbf{2}}$?

Figure 21-16 shows three situations involving a charged particle and a uniformly charged spherical shell. The charges are given, and the radii of the shells are indicated. Rank the situations according to the magnitude of the force on the particle due to the presence of the shell, greatest first.

In Fig. 21-24, three identical conducting spheres initially have the following charges: sphere A,$\mathbf{4}\mathbf{Q}$ ; sphere B,$\mathbf{-}\mathbf{6}\mathbf{Q}$ ; and sphere C,$\mathbf{0}$ . Spheres Aand Bare fixed in place, with a center-to-center separation that is much larger than the spheres. Two experiments are conducted. In experiment 1, sphere Cis touched to sphere Aand then (separately) to sphere B, and then it is removed. In experiment 2, starting with the same initial states, the procedure is reversed: Sphere Cis touched to sphere Band then (separately) to sphere A, and then it is removed. What is the ratio of the electrostatic force between Aand Bat the end of experiment 2 to that at the end of experiment 1?

Figure 21-17 shows four arrangements of charged particles. Rank the arrangements according to the magnitude of the net electrostatic force on the particle with charge$\mathbf{+}\mathbf{Q}$, greatest first.

Two identical conducting spheres, fixed in place, attract each other with an electrostatic force of 0.108Nwhen their center-to-center separation is50.0cm. The spheres are then connected by a thin conducting wire. When the wire is removed, the spheres repel each other with an electrostatic force of 0.0360N. Of the initial charges on the spheres, with a positive net charge, what were (a) the negative charge on one of them and (b) the positive charge on the other?

Figure 21-18 shows four situations in which particles of charge $\mathbf{+}\mathit{q}$or $\mathbf{-}\mathit{q}$are fixed in place. In each situation, the particles on the xaxis are equidistant from the yaxis. First, consider the middle particle in situation 1; the middle particle experiences an electrostatic force from each of the other two particles. (a) Are the magnitudes Fof those forces the same or different? (b) Is the magnitude of the net force on the middle particle equal to, greater than, or less than 2F? (c) Do the xcomponents of the two forces add or cancel? (d) Do their ycomponents add or cancel? (e) Is the direction of the net force on the middle particle that of the canceling components or the adding components? (f) What is the direction of that net force? Now consider the remaining situations: What is the direction of the net force on the middle particle in (g) situation 2, (h) situation 3, and (i) situation 4? (In each situation, consider the symmetry of the charge distribution and determine the canceling components and the adding components.)