Chapter 15: Q8Q (page 616)
Explain briefly how knowing the electric field of a ring helps in calculating the field of a disk.
Answer
The disk can be divided into tiny rings and the electric fields of the tiny rings can be added to get the electric field of the desk.
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For a disk of radius R=20cm and , calculate the electric field 2 mm from the center of the disk using all three equations:
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How good are the approximate equations at this distance? For the same disk, calculate E at a distance of 5 cm (50 mm) using all three equations. How good are the approximate equations at this distance?
A thin-walled hollow circular glass tube, open at both ends, has a radius R and length L. The axis of the tube lies along the x axis, with the left end at the origin (Figure 15.58). The outer sides are rubbed with silk and acquire a net positive charge Q distributed uniformly. Determine the electric field at a location on the x axis, a distance w from the origin. Carry out all steps, including checking your result. Explain each step. (You may have to refer to a table of integrals.)
An electrostatic dust precipitator that is installed in a factory smokestack includes a straight metal wire of length L=0.8 mthat is charged approximately uniformly with a total charge . A speck of coal dust (which is mostly carbon) is near the wire, far from both ends of the wire; the distance from the wire to the speck is d=1.5 cm . Carbon has an atomic mass of 12( 6protons and 6neutrons in the nucleus). A careful measurement of the polarizability of a carbon atom gives the value
(a) Calculate the initial acceleration of the speck of coal dust, neglecting gravity. Explain your steps clearly. Your answer must be expressed in terms ofand . You can use other quantities in your calculations, but your final result must not include them. Donโt put numbers into your calculation until the very end, but then show the numerical calculation that you carry out on your calculator. It is convenient to use the โbinomial expansionโ that you may have learned in calculus, thatis . Note thatcan be negative. (b) If the speck of coal dust were initially twice as far from the charged wire, how much smaller would be the initial acceleration of the speck?
A thin rod lies on the x axis with one end atand the other end at, as shown in Figure 15.51. A charge of
is spread uniformly over the surface of the rod. We want to set up an integral to find the electric field at location due to the rod. Following the procedure discussed in this chapter, we have cut up the rod into small segments, each of which can be considered as a point charge. We have selected a typical piece, shown in red on the diagram
Answer using the variables as appropriate. Remember that the rod has charge. (a) In terms of the symbolic quantities given above and on the diagram, what is the charge per unit length of the rod? (b) What is the amount of chargeon the small piece of length? (c) What is the vector from this source to the observation location? (d) What is the distance from this source to the observation location? (e) When we set up an integral to find the electric field at the observation location due to the entire rod, what will be the integration variable?
A solid plastic sphere of radius has a charge on its surface (Figure 15.70). A concentric spherical metal shell of inner radius and outer radius carries a charge on the inner surface and a charge on the outer surface. , , and are positive numbers, and the total charge on the metal shell is greater than .
At an observation location a distance from the center, determine the magnitude and direction of the electric field in the following regions, and explain briefly in each case. For parts role="math" localid="1656931802199" , be sure to give both the direction and the magnitude of the electric field, and explain briefly: (a)role="math" localid="1656932347681" (inside the plastic sphere), (b)role="math" localid="1656932286893" (in the air gap), (c)role="math" localid="1656932322994" (in the metal),(d)role="math" localid="1656932390135" (outside the metal).(e) Supposerole="math" localid="1656932377163" . What isrole="math" localid="1656932400004" ? Explain fully on the basis of fundamental principles. (f) What can you say about the molecular polarization in the plastic? Explain briefly. Include a drawing if appropriate.
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