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Chapter 15: Q12Q (page 616)
Define 鈥渇ringe field.鈥�
Fringe field is described as the peripheral field of magnet that remains outside the magnetic core.
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Question: A glass sphere carrying a uniformly distributed charge of is surrounded by an initially neutral spherical plastic shell (Figure 15.67).
(a) Qualitatively, indicate the polarization of the plastic. (b) Qualitatively, indicate the polarization of the inner glass sphere. Explain briefly. (c) Is the electric field at location P outside the plastic shell larger, smaller, or the same as it would be if the plastic weren鈥檛 there? Explain briefly. (d) Now suppose that the glass sphere carrying a uniform charge of is surrounded by an initially neutral metal shell (Figure 15.68). Qualitatively, indicate the polarization of the metal.
e) Now be quantitative about the polarization of the metal sphere and prove your assertions. (f) Is the electric field at location outside the metal shell larger, smaller, or the same as it would be if the metal shell weren鈥檛 there? Explain briefly.
In Figure 15.61 are two uniformly charged disks of radius R that are very close to each other (gap鈮猂). The disk on the left has a charge of鈭�and the disk on the right has a charge of +(is greater than). A uniformly charged thin rod of length L lies at the edge of the disks, parallel to the axis of the disks and cantered on the gap. The rod has a charge of +.
(a) Calculate the magnitude and direction of the electric field at the point marked 脳 at the center of the gap region, and explain briefly, including showing the electric field on a diagram. Your results must not contain any symbols other than the given quantities R,, , L, and(and fundamental constants), unless you define intermediate results in terms of the given quantities. (b) If an electron is placed at the center of the gap region, what are the magnitude and direction of the electric force that acts on the electron?
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.
A disk of radius 16 cm has a total charge 4 脳 10鈭�6 C distributed uniformly all over the disk. (a) Using the exact equation, what is the electric field 1 mm from the center of the disk? (b) Using the same exact equation, find the electric field 3 mm from the center of the disk. (c) What is the percent difference between these two numbers?
Consider the algebraic expression for the electric field of a uniformly charged ring, at a location on the axis of the ring. Q is the charge on the entire ring, and is the charge on one piece of the ring. is the angle subtended by one piece of the ring (or, alternatively, is the arc length of one piece). What is, expressed in terms of given constants and an integration variable? What are the integration limits?
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