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Electric Field Calculations for Continuous Charge Distributions

Solve problems involving electric field calculations for continuous charge distributions. Examples include determining field magnitude from long line of charge and uniform disk.

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Electric Field Calculations for Continuous Charge Distributions

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  1. Chapter 21, Electric Charge, and electric Field

  2. 21-7 Electric Field Calculations for Continuous Charge Distributions Example 21-11: Long line of charge. Determine the magnitude of the electric field at any point P a distance x from a very long line (a wire, say) of uniformly distributed charge. Assume x is much smaller than the length of the wire, and let λ be the charge per unit length (C/m). https://www.wolframalpha.com/input/?i=integrate+dy%2F(x%5E2%2By%5E2)%5E(3%2F2)+from+-infinity+to+infinity

  3. Problem 31 31.(II) A long uniformly charged thread (linear charge density λ =2.5C/m) lies along the x axis in Fig. 21–56. A small charged sphere (Q=-2.0C) is at the point x=0cm, y=-5.0cm. What is the electric field at the point x=7.0cm and y=7.0cm? Ethread and EQ represent fields due to the long thread and the charge Q, respectively.

  4. 21-7 Electric Field Calculations for Continuous Charge Distributions Example 21-12: Uniformly charged disk. Charge is distributed uniformly over a thin circular disk of radius R. The charge per unit area (C/m2) is σ. Calculate the electric field at a point P on the axis of the disk, a distance z above its center. https://www.wolframalpha.com/input/?i=integrate+x+*(x%5E2%2Ba)%5E(-3%2F2)+dx

  5. 21-7 Electric Field Calculations for Continuous Charge Distributions In the previous example, if we are very close to the disk (that is, if z << R), the electric field is: This is the field due to an infinite plane of charge.

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