Chapter 21: Coulomb’s Law

In Fig. 21-26, particles 1 and 2 are fixed in place on an xaxis, at a separation of$\mathit{L}\mathbf{=}\mathbf{8}\mathbf{.}\mathbf{00}\mathbf{}\mathit{c}\mathit{m}$.Their charges are ${\mathit{q}}_{\mathbf{1}}\mathbf{=}\mathbf{+}\mathit{e}\mathbf{}$and${\mathit{q}}_{\mathbf{2}}\mathbf{=}\mathbf{-}\mathbf{27}\mathit{e}$. Particle 3 with charge${\mathit{q}}_{\mathbf{3}}\mathbf{=}\mathbf{+}\mathbf{4}$is to be placed on the line between particles 1 and 2, so that they produce a net electrostatic force${\overrightarrow{\mathbf{F}}}_{\mathbf{3}\mathbf{,}\mathbf{n}\mathbf{e}\mathbf{t}}$on it. (a) At what coordinate should particle 3 be placed to minimize the magnitude of that force? (b) What is that minimum magnitude?

Earth’s atmosphere is constantly bombarded by cosmic ray protonsthat originate somewhere in space. If the protons all passed through the atmosphere, each square meter of Earth’s surface would intercept protons at the average rate of$\mathbf{1500}$ protons per second. What would be the electric current intercepted by the total surface area of the planet?

Figure 21-34ashows charged particles 1 and 2 that are fixed in place on an x-axis. Particle 1 has a charge with a magnitude of$\mathbf{\left|}{\mathbf{q}}_{\mathbf{1}}\mathbf{\right|}\mathbf{}\mathbf{=}\mathbf{}\mathbf{8.00}\mathbf{e}$. Particle 3 of charge${\mathbf{q}}_{\mathbf{3}}\mathbf{=}\mathbf{+}\mathbf{8}\mathbf{.00}\mathbf{e}$is initially on the x-axis near particle 2.Then particle 3 is gradually moved in the positive direction of the x-axis. As a result, the magnitude of the net electrostatic force on particle 2 due to particles 1 and 3

changes. Figure 21-34bgives the xcomponent of that net force as a function of the position xof particle 3.The scale of the x-axis is setby ${\mathbf{x}}_{\mathbf{s}}\mathbf{}\mathbf{=}\mathbf{}\mathbf{0}\mathbf{.80}\mathbf{\text{m}}$. Theplot has an asymptote of${\mathbf{F}}_{\mathbf{2}\mathbf{net}}\mathbf{=}\mathbf{}\mathbf{1}\mathbf{.5}\mathbf{}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{25}}\mathbf{\text{\hspace{0.17em}N}}$as$\mathit{x}\mathbf{}\mathbf{\to }\mathit{\infty }$. As a multiple of eand including the sign, what is the charge${\mathbf{q}}_{\mathbf{2}}$of particle 2?

Calculate the number of coulombs of positive charge in $\mathbf{250}\mathbf{}{\mathbf{cm}}^{\mathbf{3}}$of (neutral) water.

Figure 21-35 shows electrons 1 and 2 on an xaxis and charged ions 3 and 4 of identical charge$-q$and at identical angles$\mathit{\theta }$. Electron 2 is free to move; the other three particles are fixed in place at horizontal distances Rfrom electron 2 and are intended to hold electron 2 in place. For physically possible values

of $\mathit{q}\mathbf{<}\mathbf{5}\mathit{e}$, what are the (a) smallest, (b) second smallest, and (c) third smallest values offor which electron 2 is held in place?

In crystals of the salt cesium chloride, cesium ions ${\mathbf{Cs}}^{\mathbf{+}}$form the eight corners of a cube and a chlorine ion ${\mathbf{Cl}}^{\mathbf{-}}$is at the cube’s center (Fig. 21-36). The edge length of the cube is $\mathbf{0.40}\mathbf{\text{nm}}$. The ${\mathbf{Cs}}^{\mathbf{+}}$ions are each deficient by one electron (and thus each has a charge of role="math" localid="1661790179659" $\mathbf{-}\mathbf{e}$), and the ${\mathbf{Cl}}^{\mathbf{-}}$ion has one excess electron (and thus has a charge of $\mathbf{-}\mathbf{e}$). (a)What is the magnitude of the net electrostatic force exerted on the ${\mathbf{Cl}}^{\mathbf{-}}$ion by the eight ${\mathbf{Cs}}^{\mathbf{+}}$ions at the corners of the cube? (b) If one of the${\mathbf{Cs}}^{\mathbf{+}}$ions is missing, the crystal is said to have a defect; what is the magnitude of the net electrostatic force exerted on the${\mathbf{Cl}}^{\mathbf{-}}$ion by the seven remaining${\mathbf{Cs}}^{\mathbf{+}}$ions?

Question: Identify X in the following nuclear reactions:

(a) ${}^{1}H+{}^{9}Be\to X+n;\left(b\right){}^{12}C+{}^{1}H\to X;\left(c\right){}^{15}N+{}^{1}H\to {}^{4}He+X.$Appendix F will help.

Figure 21-37 shows four identical conducting spheres that are actually well separated from one another. Sphere W(with an initial charge of zero) is touched to sphere Aand then they are separated. Next, sphere Wis touched to sphere B(with an initial charge of$\mathbf{-}\mathbf{32}\mathbf{e}$) and then they are separated. Finally, sphere Wis touched to sphere C(with an initial charge of$\mathbf{-}\mathbf{48}\mathbf{e}$), and then they are separated. The final charge on sphere Wis$\mathbf{-}\mathbf{18}\mathbf{e}$.What was the initial charge on sphere A?

In Fig. 21-38, particle 1 of charge $\mathbf{+}\mathbf{4}\mathbf{e}$is above a floor by distance ${\mathbf{d}}_{\mathbf{1}}\mathbf{=}\mathbf{}\mathbf{2.00}\mathbf{\text{mm}}$and particle 2 of charge$\mathbf{\text{+6e}}$is on the floor, at distance${\mathit{d}}_{\mathbf{2}}\mathbf{=}\mathbf{}\mathbf{6.00}\mathbf{\text{mm}}$horizontally from particle 1.What is the xcomponent of the electrostatic force on particle 2 due to particle 1?

What must be the distance between point charge ${\mathit{q}}_1\mathbf{=}\mathbf{26}\mathbf{.}\mathbf{0}\mathit{\mu }\mathit{c}$ and point chargerole="math" localid="1661869629566" ${\mathit{q}}_{\mathbf{2}}\mathbf{=}\mathbf{-}\mathbf{47}\mathbf{.}\mathbf{0}\mathit{\mu }\mathit{c}$ for the electrostatic force between them to have a magnitude of 5.70 N ?