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...

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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.
A cylindrical shell of radius 7.00 cm and length 2.40 m has its charge uniformly distributed on its curved surface. The magnitude of the electric field at a point 19.0 cm radially outward from its axis (measured from the midpoint of the shell) is 36.0 kN/C. Find (a) the net charge on the shell and (b) the electric field at a point 4.00 cm from the axis, measured radially outward from the midpoint of the shell.
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?
An infinitely long line charge having a uniform charge per unit length lies a distance d from point O as shown in Figure P24.17. Determine the total electric flux through the surface of a sphere of radius R centered at O resulting from this line charge. Consider both cases, where (a) R d and (b) R d.
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 dosed surface with dimensions a = b= 0.400 111 and c = 0.600 in is located as shown in Figure 124.63. The left edge of the closed surface is located at position x = a. The electric field throughout the region is non- uniform and is given by E = (3.00 + 2.00x2)i N/C, where x is in meters. (a) Calculate the net electric flux leaving the closed surface. (b) What net charge enclosed by the surface?
A charge of 1.70 102 C is at the center of a cube of edge 80.0 cm. No other charges are nearby. (a) Find the flux through the whole surface of the cube. (b) Find the flux through each face of the cube. (c) Would your answers to parts (a) or (b) change if the charge were not at the center? Explain.
A long cylinder of copper of radius 3 cm is charged so that it has a uniform charge per unit length on its surface of 3 C/m. (a) Find the electric field inside and outside the cylinder. (b) Draw electric field lines in a plane perpendicular to the rod.
A particle with charge Q is located on the axis of a circle of radius R at a distance b from the plane of the circle (Fig. P23.48). Show that if one-fourth of the electric flux from the charge passes through the circle, then R=3b. Figure P23.48
The electric field at a point on the perpendicular bisector of a charged rod was calculated as the first example of a continuous charge distribution, resulting in Equation 24.15:E=kQy12+y2j a. Find an expression for the electric field when the rod is infinitely long. b. An infinitely long rod with uniform linear charge density also contains an infinite amount of charge. Explain why this still produces an electric field near the rod that is finite.
Figure P15.49 shows a closed cylinder with cross-sectional area A = 2.00 m2. The constant electric field E has magnitude 3.50 103 N/C and is directed vertically upward, perpendicular to the cylinder's top and bottom surfaces so that no field lines paw through the curved surface. Calculate the electric flux through the cylinder's (a) lop and (b) bottom surface, (c) Determine the amount of charge inside the cylinder. Figure P15.49
Two infinite, nonconducting sheets of charge are parallel to each other as shown in Figure P19.73. The sheet on the left has a uniform surface charge density , and the one on the right hits a uniform charge density . Calculate the electric field at points (a) to the left of, (b) in between, and (c) to the right of the two sheets. (d) What If? Find the electric fields in all three regions if both sheets have positive uniform surface charge densities of value .