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Chapter 24 electric flux

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Chapter 24 electric flux

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    1. 1 Norah Ali Al-moneef King Saud university

    2. 2 Norah Ali Al-moneef King Saud university

    3. Electric Flux Electric flux is the product of the magnitude of the electric field and the surface area, A, perpendicular to the field FE = EA 3 Norah Ali Al-moneef King Saud university

    4. The electric flux is proportional to the number of electric field lines penetrating some surface The field lines may make some angle ? with the perpendicular to the surface Then FE = EA cos ? The flux is a maximum when the surface is perpendicular to the field The flux is a minimum (zero) when the surface is (parallel) to the field 4 Norah Ali Al-moneef King Saud university

    5. Electric Flux If the field varies over the surface, F = EA cos ? is valid for only a small element of the area In the more general case, look at a small area element In general, this becomes 5 Norah Ali Al-moneef King Saud university

    6. Electric Flux The surface integral means the integral must be evaluated over the surface in question The value of the flux depends both on the field pattern and on the surface SI units: N.m2/C 6 Norah Ali Al-moneef King Saud university

    7. Electric Flux, Closed Surface For a closed surface, by convention, the A vectors are perpendicular to the surface at each point and point outward (1) ? < 90o, F > 0 (2) ? = 90o, F = 0 (3) 180o > ? > 90o, F < 0 7 Norah Ali Al-moneef King Saud university

    8. 8 Norah Ali Al-moneef King Saud university

    9. 9 Norah Ali Al-moneef King Saud university

    10. Gaussian surfaces of various shapes can surround the charge (only S1 is spherical) The electric flux is proportional to the number of electric field lines penetrating these surfaces, and this number is the same Thus the net flux through any closed surface surrounding a point charge q is given by q/eo and is independent of the shape of the surface 10 Norah Ali Al-moneef King Saud university

    11. Gauss Law If the charge is outside the closed surface of an arbitrary shape, then any field line entering the surface leaves at another point Thus the electric flux through a closed surface that surrounds no charge is zero 11 Norah Ali Al-moneef King Saud university

    12. Gauss Law Since the electric field due to many charges is the vector sum of the electric fields produced by the individual charges, the flux through any closed surface can be expressed as Although Gausss law can, in theory, be solved to find for any charge configuration, in practice it is limited to symmetric situations One should choose a Gaussian surface over which the surface integral can be simplified and the electric field determined 12 Norah Ali Al-moneef King Saud university

    13. 13 Norah Ali Al-moneef King Saud university

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    15. 15 Norah Ali Al-moneef King Saud university

    16. For r > a 16 Norah Ali Al-moneef King Saud university

    17. 17 Norah Ali Al-moneef King Saud university

    18. Field Due to a Spherically Symmetric Charge Distribution Inside the sphere, E varies linearly with r (E ? 0 as r ? 0) The field outside the sphere is equivalent to that of a point charge located at the center of the sphere 18 Norah Ali Al-moneef King Saud university

    19. 19 Norah Ali Al-moneef King Saud university

    20. 20 Norah Ali Al-moneef King Saud university

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    24. 24 Norah Ali Al-moneef King Saud university

    25. 25 Norah Ali Al-moneef King Saud university

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    29. Charge Resides on the Surface Choose a Gaussian surface inside but close to the actual surface The electric field inside is zero There is no net flux through the gaussian surface Because the gaussian surface can be as close to the actual surface as desired, there can be no charge inside the surface 29 Norah Ali Al-moneef King Saud university

    30. E-Fields Magnitude and Direction Choose a cylinder as the Gaussian surface The field must be perpendicular to the surface If there were a parallel component to E, charges would experience a force and accelerate along the surface and it would not be in equilibrium 30 Norah Ali Al-moneef King Saud university

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    41. 6/11/2012 41 Norah Ali Al-moneef king saud university

    42. 6/11/2012 42 Norah Ali Al-moneef king saud university

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