{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

8B - 4_Gauss

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

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

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”

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

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

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

View Full Document
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.
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.

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

View Full Document
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
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

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

View Full Document
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.
Choosing Gaussian Surfaces Desired E : Constant over the surface (by symmetry).

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

• 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.

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

• 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.

Dana University of Pennsylvania ‘17, Course Hero Intern

• 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.

Jill Tulane University ‘16, Course Hero Intern