There is a spherical hole inside the ball that is uniformly charged with a volume density of ρ . The center of this hole is shifted by the vector r from the center of the ball. Calculate the field vector inside the hole. Assuming the throughput is 1. The radius of the hole is a and the radius of the ball is b.(a

There is a spherical hole inside the ball that is uniformly charged with a volume density of ρ . The center of this hole is shifted by the vector r from the center of the ball. Calculate the field vector inside the hole. Assuming the throughput is 1. The radius of the hole is a and the radius of the ball is b.(a

University Physics Volume 2

18th Edition

ISBN:9781938168161

Author:OpenStax

Publisher:OpenStax

Chapter6: Gauss's Law

Section: Chapter Questions

Problem 85AP: A non-conducting spherical shell of inner radius a1 and outer radius b1 is uniformly charged with...

See similar textbooks

Similar questions

Recall that in the example of a uniform charged sphere, p0=Q/(43R3). Rewrite the answers in terms of the total charge Q on the sphere.
A non-conducting spherical shell of inner radius a1 and outer radius b1 is uniformly charged with charged density p1 inside another non-conducting spherical shell of inner radius a2 and outer radius b2 that is also uniformly charged with charge density p2 . See below. Find the electric field at space point P at a distance r from the common center such that (a) rb2 (b) a2rb2 , (c) b1ra2 , (d) a1rb1 , and (e) ra1 .
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 c as shown in Figure P19.75. 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?
Calculate the electric field due to a uniformly charged rod of length L, aligned with the x-axis with one end at the origin; at a point P on the z-axis.
A particle with charge q on the negative x axis and a second particle with charge 2q on the positive x axis are each a distance d from the origin. Where should a third particle with charge 3q be placed so that the magnitude of the electric field at the origin is zero?
The electric field 10.0 cm from the surface of a copper ball of radius 5.0 cm is directed toward the ball's center and has magnitude 4.0102 N/C. How much charge is on the surface of the ball?
An aluminum spherical ball of radius 4 cm is charged with 5C of charge. A copper spherical shell of inner radius 6 cm and outer radius 8 cm surrounds it. A total charge of 8C is put on the copper shell. (a) Find the electric field at all points in space, including points inside the aluminum and copper shell when copper shell and aluminum sphere are concentric. (b) Find the electric field at all points in space, including points inside the aluminum and copper shell when the centers of copper shell and aluminum sphere are 1 cm apart.
In the figure below, a small, nonconducting ball of mass m = 1.4 mg and charge q = 2.2 ✕ 10−8 C (distributed uniformly through its volume) hangs from an insulating thread that makes an angle θ = 27° with a vertical, uniformly charged nonconducting sheet (shown in cross-section). Considering the gravitational force of the ball and assuming that the sheet extends far vertically and into and out of the page, calculate the surface charge density σ of the sheet. ___________C/m2
An insulating sphere of radius a is placed at the center of a spherical conductor whose inner radius is b and outer radius is c (see figure). The +Q charge is uniformly distributed throughout the insulator sphere, while the spherical shell is -Q charged. Find the electric field strength E as a function of the radial distance r, a. inside the insulator ball (r<a) b. in a<r<b c. inside the spherical shell (b<r<c) d. outside the shell (r>c) e. How much charge on the inner surface of the spherical conductor (r= b), and how much on the outer surface of the spherical conductor (r = c)?
A spherical Conductor of radius 0.330 m has a spherical cavity of radius 0.120m at its center. The conductor carries a total charge of -6.00 nC; in addition, at the center of the spherical cavity is a point charge of +4.00 nC. Find (a) the total charge on the surface of the cavity, (b) the total charge on the outer surface of the condutor, (c) the magnitude of the electric field just inside te surface of the cavity, and The answers were wrong on the previous attempts, the answers should be (a) +4.00 nC (b) -4.00 nC (c) 2.5*10^3 N/C I need to know how those answers are solved
Early in the 20th century, a leading model of the structure of the atom was that of English physicist J. J. Thomson (the discoverer of the electron). In Thomson’s model, an atom consisted of a sphere of positively charged material in which were embedded negatively charged electrons, like chocolate chips in a ball of cookie dough. Consider such an atom consisting of one electron with mass m and charge -e, which may be regarded as a point charge, and a uniformly charged sphere of charge +e and radius R. By that time time, it was known that excited atoms emit light waves of only certain frequencies. In his model, the frequency of emitted light is the same as the oscillation frequency of the electron (s) problems in the atom. What radius (in millimeter) would a Thomson-model atom need for it to produce red light of frequency 4.57 x 1014 Hz? (Don't express your answer in scientific notation)
A negatively charged particle with q = -1 uC is placed at the center of the uniformly charged cube with side a=1 mm and total charge Q = 3 C spread out over all six faces of the cube. What is the total force acting on the particle in the center? Find the magnitude and the direction.