Chapter 24

# Chapter 24 - 24 Gauss's Law CHAPTER OUTLINE 24.1 24.2 24.3...

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24 CHAPTER OUTLINE 24.1 Electric Flux 24.2 Gauss’s Law 24.3 Application of Gauss’s Law to Various Charge Distributions 24.4 Conductors in Electrostatic Equilibrium 24.5 Formal Derivation of Gauss‘s Law Gauss’s Law ANSWERS TO QUESTIONS Q24.1 The luminous flux on a given area is less when the sun is low in the sky, because the angle between the rays of the sun and the local area vector, d A , is greater than zero. The cosine of this angle is reduced. The decreased flux results, on the average, in colder weather. Q24.2 If the region is just a point, line, or plane, no. Consider two protons in otherwise empty space. The electric field is zero at the midpoint of the line joining the protons. If the field-free region is three-dimensional, then it can contain no charges, but it might be surrounded by electric charge. Consider the interior of a metal sphere carrying static charge. Q24.3 The surface must enclose a positive total charge. Q24.4 The net flux through any gaussian surface is zero. We can argue it two ways. Any surface contains zero charge so Gauss’s law says the total flux is zero. The field is uniform, so the field lines entering one side of the closed surface come out the other side and the net flux is zero. Q24.5 Gauss’s law cannot tell the different values of the electric field at different points on the surface. When E is an unknown number, then we can say Ed A E d A cos cos θθ zz = . When Ex y z ,, bg is an unknown function, then there is no such simplification. Q24.6 The electric flux through a sphere around a point charge is independent of the size of the sphere. A sphere of larger radius has a larger area, but a smaller field at its surface, so that the product of field strength and area is independent of radius. If the surface is not spherical, some parts are closer to the charge than others. In this case as well, smaller projected areas go with stronger fields, so that the net flux is unaffected. Q24.7 Faraday’s visualization of electric field lines lends insight to this question. Consider a section of a vertical sheet carrying charge +1 coulomb. It has 1 0 field lines pointing out from it horizontally to the right and left, all uniformly spaced. The lines have the same uniform spacing close to the sheet and far away, showing that the field has the same value at all distances. 29

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30 Gauss’s Law Q24.8 Consider any point, zone, or object where electric field lines begin. Surround it with a close-fitting gaussian surface. The lines will go outward through the surface to constitute positive net flux. Then Gauss’s law asserts that positive net charge must be inside the surface: it is where the lines begin. Similarly, any place where electric field lines end must be just inside a gaussian surface passing net negative flux, and must be a negative charge.
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Chapter 24 - 24 Gauss's Law CHAPTER OUTLINE 24.1 24.2 24.3...

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