ASSIGNMENT #6

DUE ON OCTOBER 20, 2005

HAND-IN

CHAPTER #23:

QUESTIONS:

8   A small charged ball lies within the hollow of a metallic spherical shell of radius R. For three situations, the net charges on the ball and shell, respectively, are (1) +4q, 0; (2) –6q, +10q; (3) +16q, –12q. Rank the situations according to the charge on (a) the inner surface of the shell and (b) the outer surface, most positive first.

PROBLEMS:

••36   In Figure 23-42a, an electron is shot directly away from a uniformly charged plastic sheet, at speed 2.0 × 10⁵ m/s. The sheet is nonconducting, flat, and very large. Figure 23-42b gives the electron's vertical velocity component v versus time t until the return to the launch point. What is the sheet's surface charge density?

••50   Figure 23-51 shows a spherical shell with uniform volume charge density = 1.84 nC/m³, inner radius a = 10.0 cm, and outer radius b = 2.00a. What is the magnitude of the electric field at radial distances (a) r = 0; (b) r = a/2.00, (c) r = a, (d) r = 1.50a, (e) r = b, and (f) r = 3.00b?

•••53   A charge distribution that is spherically symmetric but not uniform radially produces an electric field of magnitude E = Kr⁴, directed radially outward from the center of the sphere. Here r is the radial distance from that center, and K is a constant. What is the volume density of the charge distribution?

54   The chocolate crumb mystery. Explosions ignited by electrostatic discharges (sparks) constitute a serious danger in facilities handling grain or powder. Such an explosion occurred in chocolate crumb powder at a biscuit factory in the 1970s. Workers usually emptied newly delivered sacks of the powder into a loading bin, from which it was blown through electrically grounded plastic pipes to a silo for storage. Somewhere along this route, two conditions for an explosion were met: (1) The magnitude of an electric field became 3.0 × 10⁶ N/C or greater, so that electrical breakdown and thus sparking could occur. (2) The energy of a spark was 150 mJ or greater so that it could ignite the powder explosively. Let us check for the first condition in the powder flow through the plastic pipes.

Suppose a stream of negatively charged powder was blown through a cylindrical pipe of radius R = 5.0 cm. Assume that the powder and its charge were spread uniformly through the pipe with a volume charge density . (a) Using Gauss' law, find an expression for the magnitude of the electric field in the pipe as a function of radial distance r from the pipe center. (b) Does E increase or decrease with increasing r? (c) Is directed radially inward or outward? (d) For = 1.1 × 10^–3 C/m³ (a typical value at the factory), find the maximum E and determine where that maximum field occurs. (e) Could sparking occur, and if so, where? (The story continues with Problem 60 in Chapter 24.)

ONLINE

CHAPTER #23:

QUESTIONS:

PROBLEMS:

••19   An isolated conductor of arbitrary shape has a net charge of +10 × 10^–6 C. Inside the conductor is a cavity within which is a point charge q = +3.0 × 10^–6 C. What is the charge (a) on the cavity wall and (b) on the outer surface of the conductor?

••23   (a) The drum of the photocopying machine in Problem 16 has a length of 42 cm and a diameter of 12 cm. What is the total charge on the drum? (b) The manufacturer wishes to produce a desktop version of the machine. This requires reducing the drum length to 28 cm and the diameter to 8.0 cm. The electric field at the drum surface must not change. What must be the charge on this new drum?

CHAPTER #26:

QUESTIONS:

PROBLEMS:

••28   Earth's lower atmosphere contains negative and positive ions that are produced by radioactive elements in the soil and cosmic rays from space. In a certain region, the atmospheric electric field strength is 120 V/m and the field is directed vertically down. This field causes singly charged positive ions, at a density of 620 cm^–3, to drift downward and singly charged negative ions, at a density of 550 cm^–3, to drift upward (Figure 26-27). The measured conductivity of the air in that region is 2.70 × 10^–14 (Ω · m)^–1. Calculate (a) the magnitude of the current density and (b) the ion drift speed, assumed to be the same for positive and negative ions.

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