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Chapter 16: Q20P (page 663)
What is the kinetic energy of a proton that is traveling at a speed of ?
The kinetic energy of a proton is .
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An isolated large plate capacitor (not connected to anything) originally has a potential difference of 1000 V with an air gap of 2 mm. Then a plastic slab 1 mm thick, with dielectric constant 5, is inserted in the middle of the air gap as shown in figure 16.96. Calculate the following potential differences and explain your work.
A metal sphere of radius r1 carries a positive charge of amount Q. A concentric spherical metal shell with inner radius r2 and outer radius r3 surrounds the inner sphere and carries a total positive charge of amount 4Q, with some of this charge on the outer surface (at r3) and some on the inner surface (at r2).(a) How is the charge 4Q distribute on the two surfaces of the outer shell? Prove this! (b) What is the potential (relative to infinity) just outside r3 halfway between r2 and r3 just inside r2, just outside r1 and at the center?
A small metal sphere of radius r initially has a charge q0 . Then a long copper wire is connected from this small sphere to a distant, large, uncharged metal sphere of radius R. Calculate the final charge q on the small sphere and the final charge on the large sphere. You may neglect the small amount of charge on the wire. What other approximations did you make? (Think about potential鈥�)
Figure 16.60 shows a portion of a long, negatively charged rod. You need to calculate the potential difference.
(a) What is the direction of the path (+y or 鈭抷)? (b) What is the sign of ?
2 Three charged metal disks are arranged as shown in Figure 16.75 (cutaway view). The disks are held apart by insulating supports not shown in the diagram. Each disk has an area of 2.5 m2 (this is the area of one flat surface of the disk). The charge and the charge .
(a) What is the electric field (magnitude and direction) in the region between disks 1 and 2? (b) Which of the following statements are true? Choose all that apply. (1) Along a path from A to B, (2) (3) localid="1657088862802" . (c) To calculate , where should the path start and where should it end? (d) Shouldlocalid="1657089209063" be positive or negative? Why? (1) Positive, because localid="1657089087291" is opposite to the direction of . (2) Negative, because is in the same direction as . (3) Zero, because. (e) What is the potential difference ? (f) What is the potential difference ? (g) What is the potential difference ? (h) What is the potential difference ? (i) What is the potential difference? (j) The charged disks have tiny holes that allow a particle to pass through them. An electron that is traveling at a fast speed approaches the plates from the left side. It travels along a path from A to G. Since no external work is done on system of plates + electron, . Consider the following states: initial, electron at location A; final, electron at location G. (1) What is the change in potential energy of the system? (2) What is the change in kinetic energy of the electron?
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