2 Electric field above a uniformly charged squresheetFind the electric field at a large distance z above the center of a square sheetof side length a, carrying a uniform surface charge density σ. Check yourresult in the following limiting cases:1. When a → ∞, compare with the result for an infinite plane.2. When >> a, compare the result with that of a point charge.

Derivation of the Electric Field at a Distance z Above a Uniformly Charged Square LoopLet's derive…

Answered: 2 Electric field above a uniformly…

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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We have two cylindrical conductors, the inner of radius c, and outer of radius d, each infinite in extent. The outer surface of the inner conductor has a surface charge density of ps. Use Cylindrical Coordinates (p, e, z) to calculate electric flux density D. Please use "c" and "d". Please do not use "a" and "b". A. Between the two cylindrical conductors B. Outside the outer conductor.
1. A thin sheet of sides 2a and 2b lying in the xy plane and centered at the origin has a uniform charge density o (see figure). a. Using the result of Example 1 in the Chapter 23 slides, show that the electric field on the z-axis is given by of ab E = 4k,o arctan | zva² + b² + z². To get full credit you must show an appropriate differential of charge dq and explain any symmetry arguments you might have use to arrive to this result. b. What is the field in the limit a and b going to infinity? Compare your answer with the result of the What If? in Example 3 in the Chapter 23 slides. c. Using the results of part (a), find an integral expression for the electric field at an arbitrary point on the x-axis created by a cube of side 2a centered at the origin with uniform volume charge density p. You do not need to solve this integral.
4. A point charge q is placed inside a spherical conducting shell of inner radius a and outer radius b as shown below. A total charge of -4q is placed on the conducting shell. For all parts below, answer in terms of q, a, b, and fundamental constants. b a. What is an expression for the electric field for 0
1. If a Gaussian sphere encloses no charge, does it follow that E = 0 on the surface of the Gaussian sphere? Justify your answer with 1–2 sentences. 2. Charge is uniformly distributed on the surface of a non-conducting spherical shell. The sphere is then dented. Is the electric field inside of the shell different after it is dented? Justify your answer with 1–2 sentences.
5. A thick, conducting, metal shell of inner radius R1 = 0.5m and outer radius R2 = 1.5m has a net charge of (-10C). Also, a (-3C) point charge is at the origin (center). Find the surface charge density on the inner surface of the shell. 6. Same setup as problem 5. Find the magnitude of the electric field at 4 meters from the center of the shell. 7. Same setup as problem 5. Find the magnitude of the electric field at 1.1 meters from the center of the shell.
Problem #1 A hollow metal sphere of radius 4 cm has a charge of 20 nC distributed evenly on the entirety of the surface. Find the surface charge density (o).
Q1. The volume charge density of a spherical shell with inner radius a and outer radius b is given as Pv = Po/R as shown in Figure 1. Determine E in all regions. (po is a positive constant) Pu Figure 1
Problem 4: who is right? Two parallel, infinite planes of charge have charge densities +20 and -o as shown in Fig. 1 They are at a distance L, from each other. Three students are asked to determine the electric field at points A and B, at a distance L above the top plane, and at a distance L below the bottom plane, respectively, as shown in the figure. Each student comes up with a different answer and a different explanation. Read carefully their statements below. The students are reminded that the electric field magnitude of an infinite plane of charge with charge density a is E = . +26 3+26 Figure 1: Two cquivalent views of the two infinite parallel planes • Student 1 draws the sketch in Fig. 2 [top] and says: "I think from the outside we can think of the two planes as a single infinite plane with charge density +20 - o =0, so then we know the electric field must be a/(2) pointing upwards at point A and also o/(2c) pointing doumwards at B". • Student 2 draws the sketch in Fig. 2…
A line charge is parallel to a perfectly conducting plate. This line charge is a distance (d) from the plate and has a charge density pl. 1. What is the voltage everywhere? 2. Find the electric field everywhere? 3. What is the surface charge density on the plate (ps)?
2. Let D = 2xyā, + 2(x² + z?)a, + 4yzā, C/m² and evaluate surface integrals to find the total charge enclosed in the rectangular parallelepiped
A charge of 140 μC is at the center of a cube of edge 45.0 cm. No other charges are nearby. (a) Find the flux through each face of the cube. Nm²/c (b) Find the flux through the whole surface of the cube. N . m²/c (c) Would your answers to parts (a) or (b) change if the charge were not at the center? (a) would change. O (b) would change. O Both (a) and (b) would change. O Neither would change.

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