Electric flux

9. Electric Flux

  • Consider a plane surface of area ΔS in a uniform electric field E in the space.

  • Draw a positive normal to the surface and θ be the angle between electric field E and the normal to the plane.

    Electric Flux

  • Electric flux of the electric field through the choosen surface is then
    Δφ = E ΔS cosθ

  • Corresponding to area ΔS we can define an area vector ΔS of magnitude ΔS along the positive normal. With this definition one can write electric flux as
    Δφ = E . ΔS

  • direction of area vector is always along normal to the surface being choosen.

  • Thus electric flux is a measure of lines of forces passing through the surface held in the electric field.

    Special Cases
  • If E is perpendicular to the surface i. e., parallel to the area vector then θ = 0 and
    Δφ = E ΔS cos0

  • If θ = π i. e., electric field vector is in the direction opposite to area vector then
    Δφ = - E ΔS

  • If electric field and area vector are perpendicular to each other then θ = π/2 and Δφ = 0

  • Flux is an scaler quantity and it can be added using rules of scaler addition.

  • For calculating total flux through any given surface , divide the surface into small area elements. Calculate the flux at each area element and add them up.

  • Thus total flux φ through a surface S is
    φ ≅ ΣE.ΔS

  • This quantity is mathematically exact only when you take the limit ΔS→0 and the sum in equation 3 is written as integral
    φ = ∫ΣE.dS

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