91Ó°ÊÓ

We know that the negative charge on the electron and the positive charge on the proton are equal. Suppose, however, that these magnitudes differ from each other by $\mathbf{0}\mathbf{.00010}\mathit{\%}\mathbf{.}$with what force would two copper coins, placed$\mathbf{1}\mathbf{.}\mathbf{0}\mathbf{}\mathit{m}$apart, repel each other? Assume that each coin contains$\mathbf{3}\mathbf{}\mathbf{×}\mathbf{}{\mathbf{10}}^{\mathbf{22}}$copperatoms. Whatdo you conclude?

In Fig. 21-26, particle 1 of charge $q_1=−80.0\text{μ°ä}$and particle 2 of charge $q_2=+40.0\text{μ°ä}$are held at separation $L=20.0\text{ c³¾}$on an xaxis. In unit-vector notation, what is the net electrostatic force on particle 3, of charge $q_3=20.0\text{ μ°ä}$, if particle 3 is placed at (a)$x=40.0$cm and (b) $x=80.0\text{ c³¾}$? What should be the (c) xand (d) ycoordinates of particle 3 if the net electrostatic force on it due to particles1 and 2 is zero?

What is the total charge in coulombs of$\mathbf{75}\mathbf{.0}\mathbf{\text{kg}}$of electrons?

Question: A particle of charge $\mathbf{+}\mathbf{3}\mathbf{.}\mathbf{00}\mathbf{×}{\mathbf{10}}^{\mathbf{-}\mathbf{6}}\mathbf{}\mathbf{\text{C}}$ is 12 cm distant from a second particle of charge$\mathbf{-}\mathbf{1}\mathbf{.}\mathbf{50}\mathbf{×}{\mathbf{10}}^{\mathbf{-}\mathbf{6}}\mathbf{}\mathbf{\text{C}}$ . Calculate the magnitude of the electrostatic force between the particles.

In Fig. 21-15, a central particle of charge-qis surrounded by two circular rings of charged particles. What are the magnitude and direction of the net electrostatic force on the central particle due to the other particles? (Hint:Consider symmetry.)

In Fig. 21-43, six charged particles surround particle 7 at radial distances of either $\mathit{d}\mathbf{}\mathbf{=}\mathbf{}\mathbf{1}\mathbf{.0}\mathbf{}\mathit{c}\mathit{m}$or$\mathbf{2}\mathit{d}$, as drawn. The charges are,${\mathit{q}}_{\mathbf{1}}\mathbf{=}\mathbf{+}\mathbf{2}\mathit{e}$,${\mathit{q}}_{\mathbf{2}}\mathbf{=}\mathbf{+}\mathbf{4}\mathit{e}$,${\mathit{q}}_{\mathbf{3}}\mathbf{=}\mathbf{+}\mathit{e}$,$\mathit{q}\mathbf{=}\mathbf{2}\mathit{e}$,,${\mathit{q}}_{\mathbf{5}}\mathbf{=}\mathbf{+}\mathbf{2}\mathit{e}$,${\mathit{q}}_{\mathbf{6}}\mathbf{=}\mathbf{+}\mathbf{8}\mathit{e}$, ${\mathit{q}}_{\mathbf{7}}\mathbf{=}\mathbf{+}\mathbf{6}\mathit{e}$with $\mathit{e}\mathbf{}\mathbf{=}\mathbf{}\mathbf{1}\mathbf{.60}\mathbf{}\mathbf{×}\mathbf{}{\mathbf{10}}^{\mathbf{−}\mathbf{19}}\mathit{C}$. What is the magnitude of the net electrostatic force on particle 7?

Three charged particles form a triangle: particle 1 with charge$Q1=80.0nC$is at x ycoordinates ($0,3.00mm$), particle 2 with charge$Q2$is at ($0,−3.00mm$), and particle 3 with charge$q=18.0nc$is at ($4.00mm,0$). In unit-vector notation, what is the electrostatic force on particle 3 due to the other two particles if$Q_2$is equal to (a)$80.0nC$and (b)$−80.0nC$?

In Fig. 21-44, what are the (a) magnitude and (b) direction of the net electrostatic force on particle 4 due to the other three particles? All four particles are fixed in the $\mathit{x}\mathit{y}\mathbf{−}$plane, and,${\mathit{q}}_{\mathbf{1}}\mathbf{=}\mathbf{}\mathbf{−}\mathbf{3}\mathbf{.20}\mathbf{}\mathbf{×}\mathbf{10}{\mathbf{}}^{\mathbf{−}\mathbf{19}\mathbf{\text{ }}}\mathbf{\text{C}}$,,${\mathit{q}}_{\mathbf{2}}\mathbf{=}\mathbf{}\mathbf{+}\mathbf{3}\mathbf{.20}\mathbf{}\mathbf{×}\mathbf{10}{\mathbf{}}^{\mathbf{−}\mathbf{19}}\mathbf{\text{ C}}$,${\mathit{q}}_{\mathbf{3}}\mathbf{=}\mathbf{}\mathbf{+}\mathbf{6}\mathbf{.40}\mathbf{}\mathbf{×}\mathbf{10}{\mathbf{}}^{\mathbf{−}\mathbf{19}}\mathbf{\text{ C}}$,${\mathit{q}}_{\mathbf{4}}\mathbf{=}\mathbf{}\mathbf{+}\mathbf{3}\mathbf{.20}\mathbf{}\mathbf{×}\mathbf{10}{\mathbf{}}^{\mathbf{−}\mathbf{19}}\mathbf{\text{ C}}$,${\mathit{θ}}_{\mathbf{1}}\mathbf{=}\mathbf{}\mathbf{35}{\mathbf{.0}}^{\mathbf{0}}$,${\mathit{d}}_{\mathbf{1}}\mathbf{=}\mathbf{}\mathbf{3}\mathbf{.00}\mathbf{\text{ }}\mathbf{}\mathbf{\text{cm}}$and ${\mathit{d}}_{\mathbf{2}}\mathbf{}\mathbf{=}\mathbf{}{\mathit{d}}_{\mathbf{3}}\mathbf{}\mathbf{=}\mathbf{}\mathbf{2}\mathbf{.00}\mathbf{}\mathbf{\text{ c³¾}}$.

Two point charges of$\mathbf{30}\mathbf{}\mathbf{\text{ n°ä}}$and localid="1663923530148" $\mathbf{-}\mathbf{40}\mathbf{}\mathbf{\text{ n°ä}}$are held fixed on an -axis, at the origin and at$\mathit{x}\mathbf{}\mathbf{=}\mathbf{}\mathbf{72}\mathbf{}\mathbf{\text{cm}}$ , respectively. A particle with a charge oflocalid="1663923537824" $\mathbf{\text{42 μ°ä}}$ is released from rest at $\mathit{x}\mathbf{}\mathbf{=}\mathbf{}\mathbf{28}\mathbf{}\mathbf{\text{ c³¾}}$. If the initial acceleration of the particle has a magnitude of$\mathbf{100}\mathbf{\text{ }}\mathbf{}{\mathbf{\text{km/s}}}^{\mathbf{\text{2}}}$ , what is the particle’s mass?

Two small, positively charged spheres have a combined charge of$\text{5.0}×{\text{10}}^{−5}\text{ C}$. If each sphere is repelled from the other by an electrostatic force of$\text{1.0N}$when the spheres are$\text{2.0m}$apart, what is the charge on the sphere with the smaller charge?