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Chapter 27: Q. 5 (page 762)
5. The electron drift speed is in a metal with a mean time between collisions of . What is the electric field strength?
The electric field strength is.
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The biochemistry that takes place inside cells depends on various elements, such as sodium, potassium, and calcium, that are dissolved in water as ions. These ions enter cells through narrow pores in the cell membrane known as ion channels. Each ion channel, which is formed from a specialized protein molecule, is selective for one type of ion. Measurements with microelectrodes have shown that a diameter potassium ion channel carries a current of role="math" localid="1649134390247" .
a. How many potassium ions pass through if the ion channel opens for ?
b. What is the current density in the ion channel?
74. FIGURE CP27.74 shows a wire that is made of two equal diameter segments with conductivities and . When current passes through the wire, a thin layer of charge appears at the boundary between the segments.
a. Find an expression for the surface charge density on the boundary. Give your result in terms of , and the wire's cross-section area .
b. A -mm-diameter wire made of copper and iron segments carries a current. How much charge accumulates at the boundary between the segments?
76. A thin metal cylinder of length and radius is coaxial with a thin metal cylinder of length and a larger radius . The space between the two coaxial cylinders is filled with a material that has resistivity . The two cylinders are connected to the terminals of a battery with potential difference , causing current to flow radially from the inner cylinder to the outer cylinder. Find an expression for the resistance of this device.
What is the resistance of
a. long gold wire that is in diameter?
b. A long piece of carbon with a square cross-section?
A hollow metal sphere has inner radius, outer radius , and conductivity . The currentlocalid="1648636152220" is radially outward from the inner surface to the outer surface.
a. Find an expression for the electric field strength inside the metal as a function of the radiuslocalid="1648636186845" from the center.
b. Evaluate the electric field strength at the inner and outer surfaces of a copper sphere and .
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