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Unformatted text preview: 1 Lecture 9 Applications of Gausss Law ACT: Crossed planes Which diagram corresponds to the E-field lines for these two uniformly charged infinite sheets that intersect each other as shown? + + + A B C Each sheet produces a uniform electric field. + G total E + G E G E + The total E field is uniform in each quadrant. EXAMPLE: Infinite line of charge A cable of diameter D = 3 mm and length L = 200 m has a total charge Q = 4 C uniformly distributed along its length. Find the electric field at point P, located at a distance r = 2 cm from it. r P L >> r infinite cable r >> D one-dimensional charge distribution 2 The elegant way (Gausss law) P The system has cylindrical symmetry. The Gaussian surface should be a cylinder of radius r and height h. Linear charge density: Q L = r P h r P h E Linear charge density: Q L = caps cylinder side = + caps (caps are parallel to lines) E = ( ) cylinder side 2 E r h = = enclosed q h = h = r P h Linear charge density: Q L = 2 h rhE = 2 E r = Example: Line and sheet...
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