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Unformatted text preview: Solution for Homework 4 Adding Electric Fields and Field Maps Solution to Homework Problem 4.1(Comparing Electric Field at Two Points) Problem: A point charge is placed at the origin of the Cartesian coordinate system. The electric field is found to be pointing in the + x direction with a magnitude of 1N / C at a point 3 units away from the origin in the + x direction. What are the magnitude and direction of the electric field at a second point 3 units away from the origin in the- x direction? Select One of the Following: (a) 1N / C in the + x direction (b-Answer) 1N / C in the- x direction (c) 2N / C in the + x direction (d) 2N / C in the- x direction Solution (a) Magnitude of the Electric Field: The two points are equidistant from the source charge, so the electric field will have equal magnitudes at the two points. Therefore, the size of the electric field at the second point is 1N / C . (b) Direction of the Electric Field: Also, the direction of the electric field due to a point source charge is along either the positive or negative radial direction, depending on the sign of the point charge. The electric field is pointing away from the point charge on the + x side of the charge, so it will also point away from the point charge on the- x side of the point charge. This means that the electric field will point in the- x direction at the second point. The correct answer is b. Total Points for Problem: 3 Points Solution to Homework Problem 4.2(Where Can There Be Zero Electric Field in a System With Two Charged Particles?) Problem: Two point charges are arranged as shown. In which section(s) in the figure is there some region capable of having zero electric field? Select One of the Following: (a) Section 1 only. (b) Section 2 only. (c-Answer) Section 3 only. (d) Sections 1 and 3 . (e) Sections 1 and 2 . (f) Sections 2 and 3 . (g) Sections 1 , 2 , and 3 . Section 1 Section 2 Section 3 + _ +2 Q- Q Solution 1 (a) Field in Section 2 : The fields of both charges point in the same direction in section 2 , so there cannot be zero field in the section. Section 1 Section 2 Section 3 + _ +2 Q- Q (b) Field in Section 1 : In section 1 , the fields are in opposite directions, but at all points in the section are closer to the larger charge, so the fields never completely cancel. (c) Field in Section 3 : This only leaves section 3 capable of having zero electric field. The correct answer is c. Total Points for Problem: 3 Points Solution to Homework Problem 4.3(Electric Field of Crossed Planes) Problem: Two infinite planes of charge are drawn to the right. One infinite uniform plane of charge occupies the x- y plane with charge density, xy = 3 . C / m 2 . Another infinite uniform plane of charge occupies the y- z plane with charge density, yz =- 2 . C / m 2 . Compute the electric field at vector r = (1 . 0cm , , 1 . 0cm) ....
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