Suppose you have q = 8 µC charge placed at the orign of your coordinate system.a) Using Gauss's law, find the electric field at distance r1 = 5 m from the charge.b) Now you place a hollow conducting sphere of inner radius a = 2.5 m and outer radius b = 10.0 m. Calculate the net enclosed charge by theGaussian surface of radius rị.c) Now consider another hollow conducting sphere of inner radius c = 15 m and outer radius d = 25 m. Calculate the net enclosed charge by theGaussian surface of radius r2 = 12.5 m and electric field at r2.d) Calculate the net flux through the Gaussian sphere of radius r2.e) Calculate the potential at the following distances from the point charge q and explain your result. Assume that at infinity the potential is zero, i.e.V (0) = 0.Potential at r = cGive your answer up to at least three significance digits.c+dPotential at r =Give your answer up to at least three significance digits.f) Plot electric field as a function of distance from origin for this system.g) (bonus) Plot electric potential as a function of distance from origin for this system. b,

Suppose you have q = 8 µC charge placed at the orign of your coordinate system. a) Using Gauss's law, find the electric field at distance ri = 5 m from the charge. b) Now you place a hollow conducting sphere of inner radius a = 2.5 m and outer radius b = 10.0 m. Calculate the net enclosed charge by the Gaussian surface of radius rı. c) Now consider another hollow conducting sphere of inner radius c = 15 m and outer radius d = 25 m. Calculate the net enclosed charge by the Gaussian surface of radius r2 = 12.5 m and electric field at r2.

Suppose you have q = 8 µC charge placed at the orign of your coordinate system. a) Using Gauss's law, find the electric field at distance ri = 5 m from the charge. b) Now you place a hollow conducting sphere of inner radius a = 2.5 m and outer radius b = 10.0 m. Calculate the net enclosed charge by the Gaussian surface of radius rı. c) Now consider another hollow conducting sphere of inner radius c = 15 m and outer radius d = 25 m. Calculate the net enclosed charge by the Gaussian surface of radius r2 = 12.5 m and electric field at r2.

Physics for Scientists and Engineers

10th Edition

ISBN:9781337553278

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter23: Continuous Charge Distributions And Gauss's Law

Section: Chapter Questions

Problem 5P: Example 23.3 derives the exact expression for the electric field at a point on the axis of a...

See similar textbooks

Similar questions

Example 23.3 derives the exact expression for the electric field at a point on the axis of a uniformly charged disk. Consider a disk of radius R = 3.00 cm having a uniformly distributed charge of +5.20 C. (a) Using the result of Example 23.3, compute the electric field at a point on the axis and 3.00 mm from the center. (b) What If? Explain how the answer to part (a) compares with the field computed from the near-field approximation E = /20. (We derived this expression in Example 23.3.) (c) Using the result of Example 23.3, compute the electric field at a point on the axis and 30.0 cm from the center of the disk. (d) What If? Explain how the answer to part (c) compares with the electric field obtained by treating the disk as a +5.20-C charged particle at a distance of 30.0 cm.
The electric field everywhere on the surface of a charged sphere of radius 0.230 m has a magnitude of 575 N/C and points radially outward from the center of the sphere. (a) What is the net charge on the sphere? (b) What can you conclude about the nature and distribution of charge inside the sphere?
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 long, straight wire is surrounded by a hollow metal cylinder whose axis coincides with that of the wire. The wire has a charge per unit length of , and the cylinder has a net charge per unit length of 2. From this information, use Gausss law to find (a) the charge per unit length on the inner surface of the cylinder, (b) the charge per unit length on the outer surface of the cylinder, and (c) the electric field outside the cylinder a distance r from the axis.
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.
The nonuniform charge density of a solid insulating sphere of radius R is given by = cr2 (r R), where c is a positive constant and r is the radial distance from the center of the sphere. For a spherical shell of radius r and thickness dr, the volume element dV = 4r2dr. a. What is the magnitude of the electric field outside the sphere (r R)? b. What is the magnitude of the electric field inside the sphere (r R)?
(a) Consider a uniformly charged, thin-walled, right circular cylindrical shell having total charge Q, radius R, and length . Determine the electric field at a point a distance d from the right side of the cylinder as shown in Figure P23.9. Suggestion: Use the result of Example 23.2 and treat the cylinder as a collection of ring charges. (b) What If? Consider now a solid cylinder with the same dimensions and carrying the same charge, uniformly distributed through its volume. Use the result of Example 23.3 to find the field it creates at the same point. Figure P23.9
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 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) The questions below are about charged disk. i. Calculate the magnitude of the electric field a distance of y = 2.0 m from a disk of radius R = 2.0 cm that has a total charge of 5.0 µC using the electric field formula for charged disk. ii. Then, calculate the magnitude of the electric field at y = 2.0 m, assuming that the charged disk is a particle of the same total charge at the origin. Compare your answers for i and ii above. 111.
Negative charge -Q is distributed uniformly around a quarter-circle of radius a that lies in the first quadrant, with the center of curvature at the origin. Part A: Find the x-component of the net electric field at the origin. Part B: Find the y-component of the net electric field at the origin. Express your answer in terms of the variables Q , a and appropriate constants.
A -1.11 nC point charge is located inside a cavity of a hollow sphere of conducting material with charge 6.72 nC and of radius 10.0 cm. Calculate the electric field 0.473 m from the point charge in units of N/C. Assume answers are in the radial direciton such that if the field points radially away your answer will be positive and if the field points radially in your answer will be negative. Give your numerical result to 3 significant figures and type in the units after your numerical answer.