Lecture 09 - Examples of Gauss s law

# Lecture 09 - Examples of Gauss s law - 1 Lecture 9...

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Unformatted text preview: 1 Lecture 9 Applications of Gauss’s 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? + σ + σ + σ − σ − σ − σ A B C Each sheet produces a uniform electric field. σ + σ G total E + G E − G E + σ σ − σ The total E field is uniform in each quadrant. − σ 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 (Gauss’s 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 λ = r P h r P h E Linear charge density: Q L λ = caps cylinder side Φ = Φ + Φ caps (caps are parallel to lines) E Φ = ( ) cylinder side 2 E r h π Φ = Φ = enclosed q h λ = h λ ε Φ = r P h Linear charge density: Q L λ = 2 h rhE λ π ε = 2 E r λ π ε = Example: Line and sheet...
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Lecture 09 - Examples of Gauss s law - 1 Lecture 9...

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