Chapter 21: Coulomb’s Law

The initial charges on the three identical metal spheres in Fig. 21-24 are the following: sphere A, $\mathit{Q}$; sphere B, $\mathbf{-}\mathit{Q}\mathbf{/}\mathbf{4}$; and sphere C, $\mathit{Q}\mathbf{/}\mathbf{2}$, where $\mathit{Q}\mathbf{}\mathbf{=}\mathbf{2}\mathbf{.00}\mathbf{}\mathbf{\times }\mathbf{}{\mathbf{10}}^{\mathbf{-}\mathbf{14}}\mathbf{}\mathit{C}$. Spheres Aand Bare fixed in place, with a center-to-center separation of $\mathit{d}\mathbf{}\mathbf{=}\mathbf{}\mathbf{1}\mathbf{.20}\mathbf{}\mathit{m}$, which is much larger than the spheres. Sphere Cis touched first to sphere Aand then to sphere Band is then removed. What then is the magnitude of the electrostatic force between spheres Aand B?

An electron is in a vacuum near Earth’s surface and located at$\mathit{y}\mathbf{}\mathbf{=}\mathbf{}\mathbf{0}$on a vertical yaxis. At what value of yshould a second electronbe placed such that its electrostatic force on the first electron balancesthe gravitational force on the first electron?

In Fig. 21-26, particle 1 of charge$\mathbf{-}\mathbf{5}\mathbf{.}\mathbf{00}\mathit{q}$and particle 2 of charge $\mathbf{+}\mathbf{}\mathbf{2}\mathbf{.}\mathbf{00}\mathit{q}$ are held at separation Lon anx-axis. If particle 3 of unknown charge q₃is to be located such that the net electrostatic force on it from particles 1 and 2 is zero, what must be the (a) x and (b) y coordinates of particle 3?

Two engineering students, John with a mass of $\mathbf{90}\mathbf{}\mathbf{\text{\hspace{0.17em}kg}}$and Mary with a mass of$\mathbf{45}\mathbf{}\mathbf{\text{\hspace{0.17em}kg}}$, are$\mathbf{30}\mathbf{\text{m}}$apart. Suppose each has a$\mathbf{0}\mathbf{.01}\mathit{\%}$imbalance in the amount of positive and negative charge, one student being positive and the other negative.Find the order of magnitude of the electrostatic force of attraction between them by replacing each student with a sphere of water having the same mass as the student.

In the radioactive decay of Eq. 21-13, a $U^{238}$ nucleus transforms

to$T{h}^{234}$and an ejected$H{e}^4$. (These are nuclei, not atoms, and thus

electrons are not involved.) When the separation between and

4He is$9.0\times {10}^{-15}\text{m}$, what are the magnitudes of (a) the electrostatic

force between them and (b) the acceleration of the particle?

Two equally charged particles are held3.2$\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{3}}\mathit{m}$ apart and then released from rest. The initial acceleration of the first particle is observed to be 7.0m/s² and that of the second to be 9.0m/s². If the mass of the first particle is$\mathbf{6}\mathbf{.}\mathbf{3}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{7}}\mathbf{kg}\mathbf{,}$, what are (a) the mass of the second particle and (b) the magnitude of the charge of each particle?

A positively charged ball is brought close to an electrically neutral isolated conductor. The conductor is then grounded while the ball is kept close. Is the conductor charged positively, charged negatively, or neutral if (a) the ball is first taken away and then the ground connection is removed and (b) the ground connection is first removed and then the ball is taken away?

In Fig. 21-25, four particles form a square. The charges are${\mathbf{\text{q}}}_{\mathbf{\text{1}}}\mathbf{\text{=+Q}}$,${\mathbf{\text{q}}}_{\mathbf{\text{2}}}{\mathbf{\text{=q}}}_{\mathbf{\text{3}}}\mathbf{\text{=q}}$, and${\mathbf{\text{q}}}_{\mathbf{\text{4}}}\mathbf{\text{=-2.00Q}}$. What is $\frac{q}{Q}$if the net electrostatic force on particle 1 is zero?

In a spherical metal shell of radius R, an electron is shot from the center directly toward a tiny hole in the shell, through which it escapes. The shell is negatively charged with a surface charge density (charge per unit area) of.$\text{6.90}\times {\text{10}}^{-13}{\text{\hspace{0.17em}C/m}}^{\text{2}}$What is the magnitude of the electron’s acceleration when it reaches radial distances (a)$r=0.500R$and (b)$\mathbf{2}\mathbf{.00}\mathit{R}$?

An electron is projected with an initial speed${\mathit{v}}_{\mathbf{i}}\mathbf{}\mathbf{=}\mathbf{}\mathbf{3}\mathbf{.2}\mathbf{}\mathbf{\times }\mathbf{}{\mathbf{10}}^{\mathbf{5}}\mathbf{}\frac{\mathbf{\text{m}}}{\mathbf{\text{s}}}$directly toward a very distant proton that is at rest. Because the proton mass is large relative to the electron mass, assume that the proton remains at rest. By calculating the work done on the electron by the electrostatic force, determine the distance between the two particles when the electron instantaneously has speed$\mathbf{2}{\mathit{v}}_{\mathbf{i}}$.