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# Chap 22 SM - Chapter 22 The Electric Field 2 Continuous...

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93 Chapter 22 The Electric Field 2: Continuous Charge Distributions Conceptual Problems 1 [SSM] Figure 22-37 shows an L-shaped object that has sides that are equal in length. Positive charge is distributed uniformly along the length of the object. What is the direction of the electric field along the dashed 45 o line? Explain your answer. Determine the Concept The resultant field is the superposition of the electric fields due to the charge distributions along the axes and is directed along the dashed line, pointing away from the intersection of the two sides of the L-shaped object. This can be seen by dividing each leg of the object into 10 (or more) equal segments and then drawing the electric field on the dashed line due to the charges on each pair of segments that are equidistant from the intersection of the legs. 2 Positive charge is distributed uniformly along the entire length of the x axis, and negative charge is distributed uniformly along the entire length of the y axis. The charge per unit length on the two axes is identical, except for the sign. Determine the direction of the electric field at points on the lines defined by y = x and y = – x . Explain your answer. Determine the Concept The electric fields along the lines defined by y = x and y = – x are the superposition of the electric fields due to the charge distributions along the axes. The direction of the electric field is the direction of the force acting on a test charge at the point(s) of interest. Typical points are shown at two points on each of the two lines. x y x y = + + + + + + + +

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Chapter 22 94 3 True or false: ( a ) The electric field due to a hollow uniformly charged thin spherical shell is zero at all points inside the shell. ( b ) In electrostatic equilibrium, the electric field everywhere inside the material of a conductor must be zero. ( c ) If the net charge on a conductor is zero, the charge density must be zero at every point on the surface of the conductor. ( a ) True (assuming there are no charges inside the shell). ( b ) True. The charges reside on the surface of conductor. ( c ) False. Consider a spherical conducting shell. Such a surface will have equal charges on its inner and outer surfaces but, because their areas differ, so will their charge densities. 4 If the electric flux through a closed surface is zero, must the electric field be zero everywhere on that surface? If not, give a specific example. From the given information can the net charge inside the surface be determined? If so, what is it? Determine the Concept No, this is not necessarily true. The only conclusion that we can draw is that there is equal positive and negative flux. For example, the net flux through a Gaussian surface completely enclosing a dipole is zero. If the electric flux is zero through the closed surface, we can conclude that the net charge inside the surface is zero.
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Chap 22 SM - Chapter 22 The Electric Field 2 Continuous...

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