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Chapter 23: Q. 28 (page 654)
An electron traveling parallel to a uniform electric field increases its speed from over a distance of . What is the electric field strength?
The electric field strength is
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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?
A small segment of wire in FIGURE contains of charge.
a. The segment is shrunk to one-third of its original length. What is the ratio of , where are the initial and final linear charge densities?
b. A proton is very far from the wire. What is the ratio Ff /Fi of the electric force on the proton after the segment is shrunk to the force before the segment was shrunk?
c. Suppose the original segment of wire is stretched to times its original length. How much charge must be added to the wire to keep the linear charge density unchanged?
FIGURE P25.69 shows a thin rod of length L and charge Q. Find an expression for the electric potential a distance x away from the center of the rod on the axis of the rod.
A positron is an elementary particle identical to an electron except that its charge is . An electron and a positron can rotate about their center of mass as if they were a dumbbell connected by a massless rod. What is the orbital frequency for an electron and a positron apart?
An electron in a vacuum chamber is fired with a speed of toward a large, uniformly charged plate away. The electron reaches a closest distance of before being repelled. What is the plate’s surface charge density?
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