Group assignment 3

INSTRUCTIONS

• You will find the text of the assignment just after these instructions.
• Writing the solution:
  • you can start the assignment 30min before the end of "övningar".
  • you will be divided in groups of 2-3 students (in breakout rooms if attend via zoom).
  • you must discuss the solution of the assignment with the 2-3 students of your group.
  • but you have to solve the assignment individually and submit your own solution.
  • use your own sheets but write your name in capital letters at the top of the sheet.
  • You can use your notes and the slides of course
  • Requirements:
    • sheets without name might be disregarded.
    • You may not use any book nor internet
    • You may not get help from anyone apart from the students in your breakout room or in your group.
    • If you attend via zoom, you must keep camera on till the end of the hour (otherwise your assignment will not be graded).
    • We might ask you to keep the microphone on.
  • Deadlines:
    
    • you have maximum 30 minutes to solve AND submit your solution via CANVAS.
    • the deadline for submission is strictly the end of the hour, despite what is written on CANVAS.
    • if you are a FUNKA student, you have 10min more (so, for FUNKA students the deadline is 10min after the end of the hour).
• Uploading the solution:
  • you need to create a pdf file (for example, with the ScanPro app, see the kurs-PM for details).
  • we accept only pdf files.
  • you need to upload the pdf file with your solution on Canvas.
• The solution is discussed at the beginning of the next class.

IMPORTANT:

• It is your responsibility to verify that the pdf file with your solution is clear and legible (this implies that also your handwriting must be legible). If the teacher can not read your text, the assignment will be graded with zero points.

Lös uppgiften och förklara varje steg.

Betrakta följande vektorfält

             $\overline{A}(\overline{r})=y^2 \hat{e}_y+z^2 \hat{e}_z$

och ytan $S$ definierad som i figuren: cylindern $S_1$ centrerad i origo med radien $R$ och höjden $2L$,  samt de två cirkelskivorna $S_2$ och $S_3$ parallella med $xy$-planet med radie $R$ placerade i $z=+L$ och $z=-L$.

1. Motivera om du kan använda Gauss sats för att beräkna flödet av $\overline{A}$ genom $S$
2. Beräkna flödet av  $\overline{A}$  genom $S$  med Gauss sats.