A dielectric spherical shell with an electric permitivity € has an inner radius R₁and an outer radius R2. The shell is charged with a total amount of chargeQ. Calculate the bound charge on the inner and outer surfaces of the shell,and then calculate the electric potential everywhere, and plot the potential asa function or radius.R2Figure 2: Dielectric spherical shell with charge Q, permittivity €, and shading.

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Answered: A dielectric spherical shell with an…

University Physics Volume 2

18th Edition

ISBN:9781938168161

Author:OpenStax

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Chapter7: Electric Potential

Section: Chapter Questions

Problem 97AP: (a) Find x L limit of the potential of a finite uniformly charged rod and show that it coincides...

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The charge density on a disk of radius R = 12.0 cm is given by = ar, with a = 1.40 C/m3 and r measured radially outward from the origin (Fig. P26.45). What is the electric potential at point A, a distance of 40.0 cm above the disk? Hint: You will need to integrate the nonuniform charge density to find the electric potential. You will find a table of integrals helpful for performing the integration.
The surface charge density on a long straight metallic pipe is . What is the electric potential outside and inside the pipe? Assume the pipe has a diameter of 2a.
At a certain distance from a charged particle, the magnitude of the electric field is 500 V/m and the electric potential is 3.00 kV. (a) What is the distance to the particle? (b) What is the magnitude of the charge?
(a) What is the potential between two points situated 10 cm and 20 cm from a 3.0C point charge? (b) To what location should the point at 20 cm be moved to increase this potential difference by a factor of two?
(a) Calculate the electric potential 0.250 cm from ail electron, (b) What is the electric potential difference between two points that are 0.250 cm and 0.750 cm from an electron? (c) How would the answers change if the electron were replaced with a proton?
In three regions of space, the electric potential is given by V(r)=0forrRV(r)=V04R2r2forRr2RV(r)=V0forr2R a. Plot V as a function of r. b. Find expressions for the electric field in all three regions. c. Plot E versus r in all three regions.
A very large sheet of insulating material has had an excess of electrons placed on it to a surface charge density of 3.00nC/m2 . (a) As the distance from the sheet increases, does the potential increase or decrease? Can you explain why without any calculations? Does the location of your reference point matter? (b) What is the shape of the equipotential surfaces? (c) What is the spacing between surfaces that differ by 1.00 V?
A uniformly charged ring with total charge q = 3.00 C and radius R = 10.0 cm is placed with its center at the origin and oriented in the xy plane. What is the difference between the electric potential at the origin and the electric potential at the point (0, 0, 30.0 cm)?
A Start with V=2k[(R2+x2)x] for the electric potential of a disk of radius R and excess surface charge density at a position x from the center of a disk on its axis, and derive an expression for the electric field at this position. Hint: See Example 24.6 (page 732) to check your answer.
Figure P26.44 shows a rod of length = 1.00 m aligned with the y axis and oriented so that its lower end is at the origin. The charge density on the rod is given by = a + by, with a = 2.00 C/m2 and b = 1.00 C /m2. What is the electric potential at point P with coordinates (0, 25.0 cm)? A table of integrals will aid you in solving this problem.
Find the electric potential at the origin given the arrangement of charged particles shown in Figure P26.7. FIGURE P26.7 Problems 7 and 28.
(a) A sphere has a surface uniformly charged with 1.00 C. At what distance from its center is the potential 5.00 MV? (b) What does your answer imply about the practical aspect of isolating such a large charge?

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