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Chapter 24

Chapter 24. Gauss’s Law (cont.). Outline. Gauss’s law (24.2) Application of Gauss’s law to various charge distributions (24.3). Gauss’s law. Gauss’s law describes a general relationship between the net electric flux through a closed surface and the charge enclosed by the surface.

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Chapter 24

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  1. Chapter 24 Gauss’s Law (cont.) PHY 1361

  2. Outline • Gauss’s law (24.2) • Application of Gauss’s law to various charge distributions (24.3) PHY 1361

  3. Gauss’s law • Gauss’s law describes a general relationship between the net electric flux through a closed surface and the charge enclosed by the surface. • Closed surface: often called a gaussian surface. PHY 1361

  4. Let’s begin with one example. • A spherical gaussian surface of radius r surrounding a point charge q. • The magnitude of the electric field everywhere on the surface of the sphere is E = keq/r2. • The electric field is  to the surface at every point on the surface. • Net electric flux through such gaussian surface is PHY 1361

  5. A non-spherical closed surface surrounding a point charge • As we discussed in the previous section, the electric flux is proportional to the number of electric field lines passing through a surface. • The number of lines through S1 is equal to the number of lines through the nonspherical surfaces S2 and S3. • The net flux through any closed surface surrounding a point charge q is given by q/0 and is independent of the shape of that surface. PHY 1361

  6. A point charge located outside a closed surface • Any electric field line that enters the surface leaves the surface at another point. • The net electric flux through a closed surface that surrounds no charge is zero. Revisit Example 24.2 PHY 1361

  7. Example: Problem #14, P. 762 • Calculate the total electric flux through the paraboloidal surface due to a constant electric field of magnitude E0 in the direction shown in the figure. PHY 1361

  8. Now let’s consider a more general case. • The net electric flux through S is E = q1/0. • The net electric flux through S’ is E = (q2 + q3)/ 0. • The net electric flux through S” is E = 0. • Charge q4 does not contribute to the flux through any surface because it is outside all surfaces. PHY 1361

  9. Gauss’s law • Gauss’s law: the net flux through any closed surface is • qin = the net charge inside the gaussian surface. • E = the (total) electric field at any point on the surface, which includes contributions from charges both inside and outside the surface. • Pitfall prevention: Zero flux is not zero field. PHY 1361

  10. Application of Gauss’s law to various charge distributions • Example 24.5 A spherically symmetric charge distribution: An insulating solid sphere of radius a has a uniform volume charge density  and carries a total positive charge Q. • (A) Calculate the magnitude of the electric field at a point outside the sphere. • (B) Find the magnitude of the electric field at a point inside the sphere. • Answer: (A) E = keQ/r2, r > a; (B) , r < a. PHY 1361

  11. Application of Gauss’s law to various charge distributions • Example 24.7 A cylindrical symmetric charge distribution: Find the electric field a distance r from a line of positive charge of infinite length and constant charge per unit length . • Answer: PHY 1361

  12. Homework • Ch. 24, P. 762, Problems: #12, 14, 29. PHY 1361

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