Chapter 18: Q13CQ (page 661)
Are the direction and magnitude of the Coulomb force unique at a given point in space? What about the electric field?
No, at a given point the coulomb force cannot be unique. Where as the magnitude and direction of electric field at a given point is unique.
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(a) Find the electric field at\(x = 5.00{\rm{ cm}}\)in Figure 18.52 (a), given that\(q = 1.00{\rm{ }}\mu C\). (b) At what position between\(3.00\)and\(8.00{\rm{ cm}}\)is the total electric field the same as that for\( - 2q\)alone? (c) Can the electric field be zero anywhere between\(0.00\)and\(8.00{\rm{ cm}}\)? (d) At very large positive or negative values of\(x\), the electric field approaches zero in both (a) and (b). In which does it most rapidly approach zero and why? (e) At what position to the right of\(11.0{\rm{ cm}}\)is the total electric field zero, other than at infinity? (Hint: A graphing calculator can yield considerable insight in this problem.)
Figure 18.52 (a) Point charges located at\[{\bf{3}}.{\bf{00}},{\rm{ }}{\bf{8}}.{\bf{00}},{\rm{ }}{\bf{and}}{\rm{ }}{\bf{11}}.{\bf{0}}{\rm{ }}{\bf{cm}}\]along the x-axis. (b) Point charges located at\[{\bf{1}}.{\bf{00}},{\rm{ }}{\bf{5}}.{\bf{00}},{\rm{ }}{\bf{8}}.{\bf{00}},{\rm{ }}{\bf{and}}{\rm{ }}{\bf{14}}.{\bf{0}}{\rm{ }}{\bf{cm}}\]along the x-axis
Find the total Coulomb force on the charge \(q\) in Figure 18.53, given that \(q = {\rm{1}}{\rm{.00 }}\mu {\rm{C}}\), \({q_a} = {\rm{2}}{\rm{.00 }}\mu {\rm{C}}\), \({q_b} = - {\rm{3}}{\rm{.00 }}\mu {\rm{C}}\), \({q_c} = - {\rm{4}}{\rm{.00 }}\mu {\rm{C}}\) , and \({q_d} = + {\rm{1}}{\rm{.00 }}\mu {\rm{C}}\). The square is \({\rm{50}}{\rm{.0 cm}}\) on a side.
When a glass rod is rubbed with silk, it becomes positive and the silk becomes negative—yet both attract dust. Does the dust have a third type of charge that is attracted to both positive and negative? Explain.
Considering Figure, suppose that qa=qd and qb=qc . First show that q is in static equilibrium. (You may neglect the gravitational force.) Then discuss whether the equilibrium is stable or unstable, noting that this may depend on the signs of the charges and the direction of displacement of qfrom the center of the square.
How many coulombs of positive charge are there in 4.00 kg of plutonium, given its atomic mass is 244 and that each plutonium atom has 94 protons?
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