A hollow conducting spherical shell with inner radius a and outer radius b carries total charge +q. A point charge +2q is placed at the center of the hollow shell. a) Find the electric field in the regions i) r b b) Find the induced charges on the surfaces i) r = a, ii) r = b. c) Find the electric potential for i) r > b, ii) a < r < b, iii)r

A hollow conducting spherical shell with inner radius a and outer radius b carries total charge +q. A point charge +2q is placed at the center of the hollow shell. a) Find the electric field in the regions i) r b b) Find the induced charges on the surfaces i) r = a, ii) r = b. c) Find the electric potential for i) r > b, ii) a < r < b, iii)r

Physics for Scientists and Engineers, Technology Update (No access codes included)

9th Edition

ISBN:9781305116399

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter24: Gauss’s Law

Section: Chapter Questions

Problem 24.46P: A thin, square, conducting plate 50.0 cm on a side lies in the xy plane. A total charge of 4.00 108...

See similar textbooks

Similar questions

Three charged particles are arranged on corners of a square as shown in Figure OQ23.11, with charge Q on both the particle at the upper left corner and the particle at the lower right corner and with charge +2Q on the particle at the lower left corner. (i) What is the direction of the electric field at the upper right corner, which is a point in empty space? (a) It is upward and to the right. (b) It is straight to the right. (c) It is straight downward. (d) It is downward and to the left. (e) It is perpendicular to the plane of the picture and outward. (ii) Suppose the +2Q charge at the lower left corner is removed. Then does the magnitude of the field at the upper right corner (a) become larger, (b) become smaller, (c) stay the same, or (d) change unpredictably?
Review. A slab of insulating material (infinite in the y and z directions) has a thickness d and a uniform positive charge density . An edge view of the slab is shown in Figure P23.45. (a) Show that the magnitude of the electric field a distance x from its center and inside the slab is E = x/0. (b) What If? Suppose an electron of charge e and mass me can move freely within the slab. It is released from rest at a distance x from the center. Show that the electron exhibits simple harmonic motion with a frequency f=12eme0 Figure P23.45
The electric field along the axis of a uniformly charged disk of radius R and total charge Q was calculated in Example 23.3. Show that the electric field at distances x that are large compared with R approaches that of a particle with charge Q = R2. Suggestion: First show that x/(x2 + R2)1/2 = (1 + R2/x2)1/2 and use the binomial expansion (1 + )n = 1 + n, when 1.
An electric dipole is located along the y axis as shown in Figure P24.48. The magnitude of its electric dipole moment is defined as p = 2aq. (a) At a point P, which is far from the dipole (r a), show that the electric potential is V=kepcosr2 (b) Calculate the radial component Er and the perpendicular component E of the associated electric field. Note that E = (1/r)(V/). Do these results seem reasonable for (c) = 90 and 0? (d) For r = 0? (e) For the dipole arrangement shown in Figure P24.48, express V in terms of Cartesian coordinates using r = (x2 + y2)1/2 and cos=y(x2+y2)1/2 (f) Using these results and again taking r a, calculate the field components Ex and Ey. Figure P24.48
Review. Two insulating spheres have radii 0.300 cm and 0.500 cm, masses 0.100 kg and 0.700 kg, and uniformly distributed charges 2.00 C and 3.00 C. They are released from rest when their centers are separated by 1.00 m. (a) How fast will each be moving when they collide? (b) What If? If the spheres were conductors, would the speeds be greater or less than those calculated in part (a)? Explain.
(a) What is the electric field 5.00 m from die center of the terminal of a Van de Graaff with a 3.00-mC charge, noting that the field is equivalent to that of a point charge at the center of the terminal? (b) At this distance, what force does the field exert on a 2.00C charge on the Van de Graaff’s belt?
A Two positively charged spheres with charges 4e and e are separated by a distance L and held motionless. A third charged sphere with charge Q is set between the two spheres and along the line joining them. The third sphere is in static equilibrium. What is the distance between the third charged sphere and the sphere that has charge 4e?
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.
Consider two identical circular rings of radius a, charged with linear and positive charge density ρL.The centers of the rings are positioned at z=d and z=-d. Consider an observation point P along the z-axis.a) Determine the electric field E = - ∇Φat point Pb) Consider the point P away from the turns (|z|>> a, d). Mathematically verify that the electric field E corresponds to that of a point charge Q.Determine the value of charge Q.c) From items a and b, determine the electrostatic potential Φ and the electric field E at z = 0
3-a) A charge Q is uniformly distributed over the volume of a solid sphere (centered at the origin)of radius R. A spherical cavity is cut out of this solid sphere, where the center of the cavity is atā = azˆ (with 0 < a < R) and the radius b of the cavity is such that a + b < R, and the chargedmaterial taken out is discarded. Determine the electrostatic potential V at a point z > R on thez-axis, assuming that V = 0 as |r| → ∞.b) Determine the electrostatic energy U stored in this sphere when the cavity is centered at theorigin, i.e. when a = 0.c) Assuming a = 0 as in part b), determine U when the radius of the cavity b → 0 and separatelywhen b → R^−. Compare these and comment on what you find.
Two large parallel plates are placed horizontally with respect to each other and are then connected to a 200V battery. If the distance beteeen the plates is 2cm, the uniform electric field between the plates is 10^4N/C in the upward direction. If the electron is released from rest at the upper plate, calculate: a) the kinetic energy of the electron after traveling 2cm to the lower plate. b) the time required for the electron to travel this distance.
An electron is projected with an initial speed vo = 1.60 x 10 m/s into the uniform field between two parallel plates, both 2.00 cm in length and is separated by a distance of 1.00 cm. Assume that the field between the plates is uniform and directed vertically downward and that the field outside the plates is zero. The elech on enters the field at a point midway between the plates. (a) If the electron just misses the upper plate as it emerges from the field, find the magnitude of the electric field. (b) Suppose that the electron is replaced by a proton with the same initial speed vo. Would the proton hit one of the plates? If not, what would be the magnitude and direction of its vertical displacement as it exits the region between the plates? If not, what would be the magnitude and direction of its vertical displacement as it exits the region between the plates?