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Chapter 17: Q18Q (page 473)
We have seen that the capacitance C depends on the size and position of the two conductors, as well as on the dielectric constant K. What then did we mean when we said that C is a constant in Eq. 17–7?
The capacitance does not rely on charge and voltage.
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Question: Near the surface of the Earth there is an electric field of about \({\bf{150}}\;{{\bf{V}} \mathord{\left/{\vphantom {{\bf{V}} {\bf{m}}}} \right.} {\bf{m}}}\)which points downward. Two identical balls with mass \({\bf{m = 0}}{\bf{.670}}\;{\bf{kg}}\) are dropped from a height of 2.00 m, but one of the balls is positively charged with \({{\bf{q}}_{\bf{1}}}{\bf{ = 650}}\;{\bf{\mu C}}\), and the second is negatively charged with \({{\bf{q}}_{\bf{2}}}{\bf{ = }} - {\bf{650}}\;{\bf{\mu C}}\). Use conservation of energy to determine the difference in the speed of the two balls when they hit the ground. (Neglect air resistance.)
If it takes an amount of work W to move two +q point charges from infinity to a distance d apart from each other, then how much work should it take to move three +q point charges from infinity to a distance d apart from each other?
(a) 2W.
(b) 3W.
(c) 4W.
(d) 6W.
In the DRAM computer chip of Problem 94, suppose the two parallel plates of one cell’s 35-fF capacitor are separated by a 2.0-nm-thick insulating material with dielectric constant K= 25.
(a) Determine the area A\(\left( {{\bf{\mu }}{{\bf{m}}^{\bf{2}}}} \right)\)of the cell capacitor’s plates.
(b) If the plate area A accounts for half of the area of each cell, estimate how many megabytes of memory can be placed on a\({\bf{3}}\;{\bf{c}}{{\bf{m}}^{\bf{2}}}\)silicon wafer.\(\left( {{\bf{1}}\;{\bf{byte = 8}}\;{\bf{bits}}{\bf{.}}} \right)\)
(II) Point a is 62 cm north of a \( - {\bf{3}}{\bf{.8}}\;{\bf{\mu C}}\) point charge, and point b is 88 cm west of the charge (Fig. 17–40). Determine (a) \({{\bf{V}}_{\bf{b}}} - {{\bf{V}}_{\bf{a}}}\) and (b) \({{\bf{\vec E}}_{\bf{b}}} - {{\bf{\vec E}}_{\bf{a}}}\) (magnitude and direction).
FIGURE 17–40 Problem 27.
Which of the following statements is valid?
(a) If the potential at a particular point is zero, the field at that point must be zero.
(b) If the field at a particular point is zero, the potential at that point must be zero.
(c) If the field throughout a particular region is constant, the potential throughout that region must be zero.
(d) If the potential throughout a particular region is constant, the field throughout that region must be zero.
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