ASSIGNMENT #7

DUE IN CLASS ON OCTOBER 27, 2005

HAND-IN

CHAPTER #23:

QUESTIONS:

PROBLEMS:

84   Figure 23-57 shows a Geiger counter, a device used to detect ionizing radiation (radiation that causes ionization of atoms). The counter consists of a thin, positively charged central wire surrounded by a concentric, circular, conducting cylindrical shell with an equal negative charge. Thus, a strong radial electric field is set up inside the shell. The shell contains a low-pressure inert gas. A particle of radiation entering the device through the shell wall ionizes a few of the gas atoms. The resulting free electrons (e) are drawn to the positive wire. However, the electric field is so intense that, between collisions with gas atoms, the free electrons gain energy sufficient to ionize these atoms also. More free electrons are thereby created, and the process is repeated until the electrons reach the wire. The resulting “avalanche” of electrons is collected by the wire, generating a signal that is used to record the passage of the original particle of radiation. Suppose that the radius of the central wire is 25 mm, the inner radius of the shell 1.4 cm, and the length of the shell 16 cm. If the electric field at the shell's inner wall is 2.9 × 10⁴ N/C, what is the total positive charge on the central wire?

CHAPTER #24:

QUESTIONS:

5   Figure 24-25 shows three sets of cross sections of equipotential surfaces; all three cover the same size region of space. (a) Rank the arrangements according to the magnitude of the electric field present in the region, greatest first. (b) In which is the electric field directed down the page?

PROBLEMS:

••16   Figure 24-34 shows a rectangular array of charged particles fixed in place, with distance a = 39.0 cm and the charges shown as integer multiples of q₁ = 3.40 pC and q₂ = 6.00 pC. With V = 0 at infinity, what is the net electric potential at the rectangle's center? (Hint: Thoughtful examination can reduce the calculation.)

••20   In Figure 24-36a, a particle of charge +e is initially at coordinate z = 20 nm on the dipole axis through an electric dipole, on the positive side of the dipole. (The origin of z is at the dipole center.) The particle is then moved along a circular path around the dipole center until it is at coordinate z = –20 nm. Figure 24-36b gives the work W_a done by the force moving the particle versus the angle that locates the particle. What is the magnitude of the dipole moment?

60   The chocolate crumb mystery. This story begins with Problem 54 in Chapter 23. (a) From the answer to part (a) of that problem, find an expression for the electric potential as a function of the radial distance r from the center of the pipe. (The electric potential is zero on the grounded pipe wall.) (b) For the typical volume charge density = –1.1 × 10^–3 C/m³, what is the difference in the electric potential between the pipe's center and its inside wall? (The story continues with Problem 50 in Chapter 25.)

ONLINE

CHAPTER #24:

PROBLEMS:

•5   Two large, parallel, conducting plates are 12 cm apart and have charges of equal magnitude and opposite sign on their facing surfaces. An electrostatic force of 3.9 × 10^–15 N acts on an electron placed anywhere between the two plates. (Neglect fringing.) (a) Find the electric field at the position of the electron. (b) What is the potential difference between the plates?

•10   As a space shuttle moves through the dilute ionized gas of Earth's ionosphere, the shuttle's potential is typically changed by –1.0 V during one revolution. Assuming the shuttle is a sphere of radius 10 m, estimate the amount of charge it collects.

CHAPTER #27:

•••14   A solar cell generates a potential difference of 0.10 V when a 500 Ω resistor is connected across it, and a potential difference of 0.15 V when a 1000 Ω resistor is substituted. What are the (a) internal resistance and (b) emf of the solar cell? (c) The area of the cell is 5.0 cm², and the rate per unit area at which it receives energy from light is 2.0 mW/cm². What is the efficiency of the cell for converting light energy to thermal energy in the 1000 Ω external resistor?

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