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Chapter 24: Q. 39 (page 684)
The earth has a vertical electric field at the surface, pointing down, that averages. This field is maintained by various atmospheric processes, including lightning. What is the excess charge on the surface of the earth
The excess charge on the surface of the earthis.
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FIGURE shows three Gaussian surfaces and the electric flux through each. What are the three charges ,and?
A hollow metal sphere hasand inner and outer radii, respectively. The surface charge density on the inside surface is . The surface charge density on the exterior surface is . What are the strength and direction of the electric field at points ,and from the center?
Newton鈥檚 law of gravity and Coulomb鈥檚 law are both inversesquare laws. Consequently, there should be a 鈥淕auss鈥檚 law for gravity.鈥� a. The electric field was defined as E u = F u on q /q, and we used this to find the electric field of a point charge. Using analogous reasoning, what is the gravitational field g u of a point mass?
Write your answer using the unit vector nr, but be careful with signs; the gravitational force between two 鈥渓ike masses鈥� is attractive, not repulsive. b. What is Gauss鈥檚 law for gravity, the gravitational equivalent of Equation 24.18? Use 桅G for the gravitational flux, g u for the gravitational field, and Min for the enclosed mass. c. A spherical planet is discovered with mass M, radius R, and a mass density that varies with radius as r = r011 - r/2R2, where r0 is the density at the center. Determine r0 in terms of M and R. Hint: Divide the planet into infinitesimal shells of thickness dr, then sum (i.e., integrate) their masses. d. Find an expression for the gravitational field strength inside the planet at distance r 6 R.
What is the net electric flux through the torus (i.e., doughnut shape) of FIGURE ?
FIGURE EX24.2 shows a cross section of two concentric spheres. The inner sphere has a negative charge. The outer sphere has a positive charge larger in magnitude than the charge on the inner sphere. Draw this figure on your paper, then draw electric field vectors showing the shape of the electric field.
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