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Chapter 23: Q. 23 (page 654)
A parallel-plate capacitor is formed from two --diameter electrodes spaced apart. The electric field strength inside the capacitor is . What is the charge (in ) on each electrode?
One electrode has charge and other one has charge.
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A ring of radius has total charge.
At what distance along the -axis is the electric field strength a maximum?
What is the electric field strength at this point?
Rank in order, from largest to smallest, the electric field strengths to at the five points inFIGURE . Explain.
A problem of practical interest is to make a beam of electrons turn a corner. This can be done with the parallel-plate capacitor shown in FIGURE. An electron with kinetic energy enters through a small hole in the bottom plate of the capacitor.
a. Should the bottom plate be charged positive or negative relative to the top plate if you want the electron to turn to the right? Explain.
b. What strength electric field is needed if the electron is to emerge from an exit hole away from the entrance hole, traveling at right angles to its original direction?
Hint: The difficulty of this problem depends on how you choose your coordinate system.
c. What minimum separation must the capacitor plates have?
The combustion of fossil fuels produces micron-sized particles of soot, one of the major components of air pollution. The terminal speeds of these particles are extremely small, so they remain suspended in air for very long periods of time. Furthermore, very small particles almost always acquire small amounts of charge from cosmic rays and various atmospheric effects, so their motion is influenced not only by gravity but also by the earth's weak electric field. Consider a small spherical particle of radius , density , and charge . A small sphere moving with speed v experiences a drag force , where is the viscosity of the air. (This differs from the drag force you learned in Chapter 6 because there we considered macroscopic rather than microscopic objects.)
a. A particle falling at its terminal speed is in equilibrium with no net force. Write Newton's first law for this particle falling in the presence of a downward electric field of strength , then solve to find an expression for .
b. Soot is primarily carbon, and carbon in the form of graphite has a density of . In the absence of an electric field, what is the terminal speed in of a -diameter graphite particle? The viscosity of air at is .
c. The earth's electric field is typically (150 N/C , downward). In this field, what is the terminal speed in of a -diameter graphite particle that has acquired 250 extra electrons?
The electric field strengthfrom the surface of adiameter metal ball is. What is the charge on the ball?
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