2. When a shower is turned on in a closed bathroom, the splashing of the water on the bare tub can fill the room's air with negatively charged ions and produce an electric field in the air as great as 1000 N/C. Consider a bathroom with dimensions 2.5 m x 3.0 m x 2.0 m. Along the ceiling, floor, and four walls, approximate the electric field in the air as being directed perpendicular to the surface and as having a uniform magnitude of 600 N/C. Also, treat those surfaces as forming a closed Gaussian surface around the room's air. What are (a) the volume charge density r and (b) the number of excess elementary charges e per cubic meter in the room's air?

2. When a shower is turned on in a closed bathroom, the splashing of the water on the bare tub can fill the room's air with negatively charged ions and produce an electric field in the air as great as 1000 N/C. Consider a bathroom with dimensions 2.5 m x 3.0 m x 2.0 m. Along the ceiling, floor, and four walls, approximate the electric field in the air as being directed perpendicular to the surface and as having a uniform magnitude of 600 N/C. Also, treat those surfaces as forming a closed Gaussian surface around the room's air. What are (a) the volume charge density r and (b) the number of excess elementary charges e per cubic meter in the room's air?

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter15: Electric Forces And Fields

Section: Chapter Questions

Problem 40P: The dome of a Van de Graaff generator receives a charge of 2.0 104 C. Find the strength of the...

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(a) Find the magnitude and direction of the electric field at the position of the 2.00 C charge in Figure P13.13. (b) How would the electric field at that point be affected if the charge there were doubled? Would the magnitude of the electric force be affected?
Lightning can be studied with a Van de Graaff generator, which consists of a spherical dome on which charge is continuously deposited by a moving belt. Charge can be added until the electric field at the surface of the dome becomes equal to the dielectric strength of air. Any more charge leaks off in sparks as shown in Figure P25.52. Assume the dome has a diameter of 30.0 cm and is surrounded by dry air with a "breakdown" electric field of 3.00 106 V/m. (a) What is the maximum potential of the dome? (b) What is the maximum charge on the dome?
(a) Find the electric field at x = 5.00 cm in Figure 18.52 (a), given that q = 1.00 C. (b) at what position between 3.00 and 8.00 cm is the total electric field the same as that for ? 2q alone? (c) Can the electric field be zero anywhere between 0.00 and 8.00 cm? (d) At very large positive or negative values of x, the electric field approaches zero in both (a) and (b). In which does it most rapidly approach zero and why? (e) At what position to the light of 11.0 cm is the total electric field zero, other than at infinity? (Hint: A graphing calculator can yield considerable insight in this problem.)
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The dome of a Van de Graaff generator receives a charge of 2.0 104 C. Find the strength of the electric field (a) inside the dome, (b) at the surface of the dome, assuming it has a radius of 1.0 m, and (c) 4.0 in front the center of the dome. Hint: See Section 15.5 to review properties of conductors in electrostatic equilibrium. Also, note that the points on the surface are outside a spherically symmetric charge distribution; the total charge may be considered to be located at the center of the sphere.
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Earth has a net charge that produces an electric field of approximately 150 N/C downward at its surface, (a) What is the magnitude and sign of the excess charge, noting the electric field of a conducting sphere is equivalent to a point charge at its center? (b) What acceleration will the field produce on a free electron near Earth’s surface? (c) What mass object with a single extra electron will have its weight supported by this field?
This afternoon, you have a physics symposium class, and you are the presenter. You will be presenting a topic to physics majors and faculty. You have been so busy that you have not had time to prepare and you dont even have an idea for a topic. You are frantically reading your physics textbook looking for an idea. In your reading, you have learned that the Earth carries a charge on its surface of about 105 C, which results in electric fields in the atmosphere. This gets you very excited about a new theory. Suppose the Moon also carries a charge on the order of 105 C, with the opposite sign! Maybe the orbit of the Moon around the Earth is due to electrical attraction between the Moon and the Earth! Theres an idea for your symposium presentation! You quickly jot down a few notes and run off to your symposium. While you are speaking, you notice one of the professors doing some calculations on a scrap of paper. Uh-oh! He has just raised his hand with a question. Why are you embarrassed?
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