Q2. A pair of concentric thin metal spheres or radius R₁ and R₂ (with R₁ < R₂) have charges Q and -Q respectively. Calculate the electric field in the region between these two sphere, i.e. for distances r from the centre where R₁

Q2. A pair of concentric thin metal spheres or radius R₁ and R₂ (with R₁ < R₂) have charges Q and -Q respectively. Calculate the electric field in the region between these two sphere, i.e. for distances r from the centre where R₁

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter24: Electric Fields

Section: Chapter Questions

Problem 63PQ: A thin, semicircular wire of radius R is uniformly charged with total positive charge Q (Fig....

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A charge of q = 2.00 109 G is spread evenly on a thin metal disk of radius 0.200 m. (a) Calculate the charge density on the disk. (b) Find the magnitude of the electric field just above the center of the disk, neglecting edge effects and assuming a uniform distribution of charge.
A thin, square, conducting plate 50.0 cm on a side lies in the xy plane. A total charge of 4.00 108 C is placed on the plate. Find (a) the charge density on each face of the plate, (b) the electric field just above the plate, and (c) the electric field just below the plate. You may assume the charge density is uniform.
A pyramid has a square base with an area of 4.00 m2 and a height of 3.5 m. Its walls are four isosceles triangles. The pyramid is in a uniform electric field of 655 N/C pointing downward (Fig. P25.13). What is the electric flux through the square base?
(a) Find the total electric field at x = 1.00 cm in Figure 18.52(b) given that q =5.00 nC. (b) Find the total electric field at x = 11.00 cm in Figure 18.52(b). (c) If the charges are allowed to move and eventually be brought to rest by friction, what will the final charge configuration be? (That is, will there be a single charge, double charge; etc., and what will its value(s) he?)
A positively charged disk of radius R = 0.0366 m and total charge 56.8 C lies in the xz plane, centered on the y axis (Fig. P24.35). Also centered on the y axis is a charged ring with the same radius as the disk and a total charge of 34.1 C. The ring is a distance d = 0.0050 m above the disk. Determine the electric field at the point P on the y axis, where P is y = 0.0100 m above the origin. FIGURE P24.35 Problems 35 and 36.
A thin, semicircular wire of radius R is uniformly charged with total positive charge Q (Fig. P24.63). Determine the electric field at the midpoint O of the diameter.
(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.)
A charged rod is curved so that it is part of a circle of radius R (Fig. P24.32). The excess positive charge Q is uniformly distributed on the rod. Find an expression for the electric field at point A in the plane of the curved rod in terms of the parameters given in the figure.
A solid, insulating sphere of radius a has a uniform charge density throughout its volume and a total charge Q. Concentric with this sphere is an uncharged, conducting, hollow sphere whose inner and outer radii are b and e as shown in Figure P24.45. We wish to understand completely the charges and electric fields at all locations. (a) Find the charge contained within a sphere of radius r a. (b) From this value, find the magnitude of the electric field for r a. (c) What charge is contained within a sphere of radius r when a r b? (d) From this value, find the magnitude of the electric field for r when a r b. (e) Now consider r when b r c. What is the magnitude of the electric field for this range of values of r? (f) From this value, what must be the charge on the inner surface of the hollow sphere? (g) From part (f), what must be the charge on the outer surface of the hollow sphere? (h) Consider the three spherical surfaces of radii a, b, and c. Which of these surfaces has the largest magnitude of surface charge density? Figure P24.45 Problems 43 and 47.
A solid plastic sphere of radius R1 = 8.00 cm is concentric with an aluminum spherical shell with inner radius R2 = 14.0 cm and outer radius R3 = 17.0 cm (Fig. P25.67). Electric field measurements are made at two points: At a radial distance of 34.0 cm from the center, the electric field has magnitude 1.70 103 N/C and is directed radially outward, and at a radial distance of 12.0 cm from the center, the electric field has magnitude 9.10 104 N/C and is directed radially inward. What are the net charges on a. the plastic sphere and b. the aluminum spherical shell? c. What are the charges on the inner and outer surfaces of the aluminum spherical shell? FIGURE P25.67
Figure P24.20 shows three charged spheres arranged along the y axis. a. What is the electric field at x = 0, y = 3.00 m? b. What is the electric field at x = 3.00 m, y = 0? FIGURE P24.20
Here’s one more model of an electron. Here e is the magnitude of the charge of an electron, and R is a constant parameter characterizing the electron’s size: rho=-e (105/4pi)r2(R-r)2/R7 , rho = 0 for r >R. a. Use the problem's symmetry to evaluate the electric field at all points in space, it r >R and r<R. b. Sketch the electric field magnitude versus r for all values of r. d. evaluate the electric potential at all points in space and sketch its magnitude as a function of r.