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Week 8, Short Day: More about Gauss’ Divergence Theorem

We will dedicate the day to a look at various types of interesting vector fields and on the fluxes they produce through open and closed surfaces. For some of these, Gauss’ Divergence Theorem will apply, but we will also see the situations in which this theorem does not apply. Also, we will consider scenarios in which the Gauss’ Theorem gives us an extraordinarily easy flux result, such as when the divergence of the given vector field is constant!

For a perspective on the usefulness of vector fields in physics – in the real world – we will consider the physical concept of conservation laws and how they guide our attention towards specific types of vector fields. Such a specific vector field of high interest and of much use is the Coulomb vector field, which we will investigate in detail.

Today’s Key Concepts

Flux and Gauss’ Divergence Theorem. The Coulomb vector field. Singularity. Conservation law.

Preparation and Syllabus

Today’s subjects are from eNote 28 Gauss’ Divergence Theorem about Flux and Gauss.

Activity Program

  • 13:00 – 14.00: $\,$ Lecture (aud. 42, b. 303A) (link to streaming)
  • 14.00 – 16.00: $\,$ Group exercises in the study areas (b. 302, bottom floor)
  • 16.00 – 17.00: $\,$ Weekly test

Group Exercises

  1. Flux through an Open vs. Closed Surface. By hand
  2. 12 Fluxes of Fields with Constant Divergence
  3. Gauss’ Theorem and Divergence
  4. Gauss’ Theorem Applied on an Open Surface!
  5. Extra Exercise 1
  6. Extra Exercise 2

Weekly Test

For all Weekly Tests, the following applies:

  • The test is an on-location test, meaning it can only be accessed in the study area.
  • No electronic aids are allowed (except for your own notes on e.g. a tablet).
  • The test can be accessed in the the Möbius quiz system via a link on DTU Learn in the module for 01006 (in the top menu click “Möbius”).
  • Your solutions to the test questions must be typed into Möbius without in-between calculations or steps. The result is automatically evaluated by Möbius.
  • To ensure a smooth experience use the Firefox or Chrome browser, and disable any add-blocker.
  • Use a DTU network.
  • You may discuss the test questions with fellow students in your study group, but you have your own version of the test with scrambled numbers that you yourself must solve and enter into Möbius.
  • During the final hour on Fridays you have one attempt. Passing this attempt will grant you 1 bonus point. From Friday at 18:00 until Wednesday at 18:00 the test is reopened for repeated attempts. Passing during this phase will grant you ½ bonus point.