{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

8B - 4_Gauss - Introduction to Gauss Law We earlier said...

Info icon This preview shows pages 1–10. Sign up to view the full content.

View Full Document Right Arrow Icon
Introduction to Gauss’ Law We earlier said that the strength of the electric field was proportional to the density of field lines. Now we show that the total number of field lines (“flux”) passing through a closed surface is proportional to the charge within the surface. This is “Gauss’ Law”
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Electric Flux  Number of lines Means related to, or proportional to E (Number of Lines) / Area = Flux / Area Flux E × Area
Image of page 2
Vector E and Area A flux is θ is the angle between v and the outward normal to A .
Image of page 3

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Area Element d A : Closed Surface Definition of direction of A : For closed surface, d A is normal to surface and points outward (from inside to outside). Φ E > 0 if E points out. Φ E < 0 if E points in.
Image of page 4
5 Open and Closed Surfaces A rectangle is an open surface — it does NOT contain a volume. A sphere is a closed surface — it DOES contain a volume.
Image of page 5

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Case II: E is constant vector field directed at angle θ to planar surface S of area A Electric Flux Φ E E d ! = " ## E A r r ˆ d dA = A n r ˆ n
Image of page 6
Electric Flux Electric flux, Φ E × Area Total flux through a closed surface: (The “dot” product means |E| | Δ A| cos θ ) For infinitesimal areas
Image of page 7

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
8 Gauss’s Law – The Idea The total “flux” of field lines penetrating any of these surfaces is the same and depends only on the amount of charge inside.
Image of page 8
Choosing Gaussian Surfaces Desired E : Constant over the surface (by symmetry).
Image of page 9

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 10
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern