Homogen geladene Kugeloberfläche
About points...
We associate a certain number of points with each exercise.
When you click an exercise into a collection, this number will be taken as points for the exercise, kind of "by default".
But once the exercise is on the collection, you can edit the number of points for the exercise in the collection independently, without any effect on "points by default" as represented by the number here.
That being said... How many "default points" should you associate with an exercise upon creation?
As with difficulty, there is no straight forward and generally accepted way.
But as a guideline, we tend to give as many points by default as there are mathematical steps to do in the exercise.
Again, very vague... But the number should kind of represent the "work" required.
When you click an exercise into a collection, this number will be taken as points for the exercise, kind of "by default".
But once the exercise is on the collection, you can edit the number of points for the exercise in the collection independently, without any effect on "points by default" as represented by the number here.
That being said... How many "default points" should you associate with an exercise upon creation?
As with difficulty, there is no straight forward and generally accepted way.
But as a guideline, we tend to give as many points by default as there are mathematical steps to do in the exercise.
Again, very vague... But the number should kind of represent the "work" required.
About difficulty...
We associate a certain difficulty with each exercise.
When you click an exercise into a collection, this number will be taken as difficulty for the exercise, kind of "by default".
But once the exercise is on the collection, you can edit its difficulty in the collection independently, without any effect on the "difficulty by default" here.
Why we use chess pieces? Well... we like chess, we like playing around with \(\LaTeX\)-fonts, we wanted symbols that need less space than six stars in a table-column... But in your layouts, you are of course free to indicate the difficulty of the exercise the way you want.
That being said... How "difficult" is an exercise? It depends on many factors, like what was being taught etc.
In physics exercises, we try to follow this pattern:
Level 1 - One formula (one you would find in a reference book) is enough to solve the exercise. Example exercise
Level 2 - Two formulas are needed, it's possible to compute an "in-between" solution, i.e. no algebraic equation needed. Example exercise
Level 3 - "Chain-computations" like on level 2, but 3+ calculations. Still, no equations, i.e. you are not forced to solve it in an algebraic manner. Example exercise
Level 4 - Exercise needs to be solved by algebraic equations, not possible to calculate numerical "in-between" results. Example exercise
Level 5 -
Level 6 -
When you click an exercise into a collection, this number will be taken as difficulty for the exercise, kind of "by default".
But once the exercise is on the collection, you can edit its difficulty in the collection independently, without any effect on the "difficulty by default" here.
Why we use chess pieces? Well... we like chess, we like playing around with \(\LaTeX\)-fonts, we wanted symbols that need less space than six stars in a table-column... But in your layouts, you are of course free to indicate the difficulty of the exercise the way you want.
That being said... How "difficult" is an exercise? It depends on many factors, like what was being taught etc.
In physics exercises, we try to follow this pattern:
Level 1 - One formula (one you would find in a reference book) is enough to solve the exercise. Example exercise
Level 2 - Two formulas are needed, it's possible to compute an "in-between" solution, i.e. no algebraic equation needed. Example exercise
Level 3 - "Chain-computations" like on level 2, but 3+ calculations. Still, no equations, i.e. you are not forced to solve it in an algebraic manner. Example exercise
Level 4 - Exercise needs to be solved by algebraic equations, not possible to calculate numerical "in-between" results. Example exercise
Level 5 -
Level 6 -
Question
Solution
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Exercise:
abcliste abc Wie sieht das elektrische Feld einer homogen geladenen Kugeloberfläche mit Radius R innerhalb r R und ausserhalb r R aus? abc Wie sieht das korrespondiere Potential zu den beiden Bereichen aus? abc Wie die elektrostatische Energie? abcliste
Solution:
abcliste abc Man verwet das Gauss'sche Gesetz: tcbhighmathaufgabeo_A vecE ddvecA fracqepsilon_ Was für r R folges ergibt: o_A vecE ddvecA fracqepsilon_ E pi r^ fracqepsilon_ Rightarrow Er fracpiepsilon_ fracqr^ Für r R ist das elektrische Feld Null. abc Fürs Potential gilt im Allgemeinen: tcbhighmathaufgabePhir _r^infty vecE ddvecr Für den Bereich r R ergibt dies dann: Phir -_infty^r vecE ddvecr -_infty^r fracpiepsilon_ fracqr^ddr fracpiepsilon_ fracqr Für den Bereich r R gilt hingegen: Phir -_infty^r vecE ddvecr -_infty^R fracpiepsilon_ fracqr^ddr-_R^r ddr fracpiepsilon_ fracqR abc Die Formel um die elektrostatische Energie zu berechnen lautet: tcbhighmathaufgabeW fracepsilon_ _^infty vecE^ ddx^ In diesem Fall führt das zu: W piepsilon_ frac_^infty E^r^ ddvecr piepsilon__^inftyfracpi^epsilon_^ fracr^r^ddr fracq^piepsilon_left_^R ddr+_r^inftyfracr^ddr fracq^piepsilon_R Dieser Ausdruck divergiert für Rrightarrow . abcliste
abcliste abc Wie sieht das elektrische Feld einer homogen geladenen Kugeloberfläche mit Radius R innerhalb r R und ausserhalb r R aus? abc Wie sieht das korrespondiere Potential zu den beiden Bereichen aus? abc Wie die elektrostatische Energie? abcliste
Solution:
abcliste abc Man verwet das Gauss'sche Gesetz: tcbhighmathaufgabeo_A vecE ddvecA fracqepsilon_ Was für r R folges ergibt: o_A vecE ddvecA fracqepsilon_ E pi r^ fracqepsilon_ Rightarrow Er fracpiepsilon_ fracqr^ Für r R ist das elektrische Feld Null. abc Fürs Potential gilt im Allgemeinen: tcbhighmathaufgabePhir _r^infty vecE ddvecr Für den Bereich r R ergibt dies dann: Phir -_infty^r vecE ddvecr -_infty^r fracpiepsilon_ fracqr^ddr fracpiepsilon_ fracqr Für den Bereich r R gilt hingegen: Phir -_infty^r vecE ddvecr -_infty^R fracpiepsilon_ fracqr^ddr-_R^r ddr fracpiepsilon_ fracqR abc Die Formel um die elektrostatische Energie zu berechnen lautet: tcbhighmathaufgabeW fracepsilon_ _^infty vecE^ ddx^ In diesem Fall führt das zu: W piepsilon_ frac_^infty E^r^ ddvecr piepsilon__^inftyfracpi^epsilon_^ fracr^r^ddr fracq^piepsilon_left_^R ddr+_r^inftyfracr^ddr fracq^piepsilon_R Dieser Ausdruck divergiert für Rrightarrow . abcliste
Meta Information
Exercise:
abcliste abc Wie sieht das elektrische Feld einer homogen geladenen Kugeloberfläche mit Radius R innerhalb r R und ausserhalb r R aus? abc Wie sieht das korrespondiere Potential zu den beiden Bereichen aus? abc Wie die elektrostatische Energie? abcliste
Solution:
abcliste abc Man verwet das Gauss'sche Gesetz: tcbhighmathaufgabeo_A vecE ddvecA fracqepsilon_ Was für r R folges ergibt: o_A vecE ddvecA fracqepsilon_ E pi r^ fracqepsilon_ Rightarrow Er fracpiepsilon_ fracqr^ Für r R ist das elektrische Feld Null. abc Fürs Potential gilt im Allgemeinen: tcbhighmathaufgabePhir _r^infty vecE ddvecr Für den Bereich r R ergibt dies dann: Phir -_infty^r vecE ddvecr -_infty^r fracpiepsilon_ fracqr^ddr fracpiepsilon_ fracqr Für den Bereich r R gilt hingegen: Phir -_infty^r vecE ddvecr -_infty^R fracpiepsilon_ fracqr^ddr-_R^r ddr fracpiepsilon_ fracqR abc Die Formel um die elektrostatische Energie zu berechnen lautet: tcbhighmathaufgabeW fracepsilon_ _^infty vecE^ ddx^ In diesem Fall führt das zu: W piepsilon_ frac_^infty E^r^ ddvecr piepsilon__^inftyfracpi^epsilon_^ fracr^r^ddr fracq^piepsilon_left_^R ddr+_r^inftyfracr^ddr fracq^piepsilon_R Dieser Ausdruck divergiert für Rrightarrow . abcliste
abcliste abc Wie sieht das elektrische Feld einer homogen geladenen Kugeloberfläche mit Radius R innerhalb r R und ausserhalb r R aus? abc Wie sieht das korrespondiere Potential zu den beiden Bereichen aus? abc Wie die elektrostatische Energie? abcliste
Solution:
abcliste abc Man verwet das Gauss'sche Gesetz: tcbhighmathaufgabeo_A vecE ddvecA fracqepsilon_ Was für r R folges ergibt: o_A vecE ddvecA fracqepsilon_ E pi r^ fracqepsilon_ Rightarrow Er fracpiepsilon_ fracqr^ Für r R ist das elektrische Feld Null. abc Fürs Potential gilt im Allgemeinen: tcbhighmathaufgabePhir _r^infty vecE ddvecr Für den Bereich r R ergibt dies dann: Phir -_infty^r vecE ddvecr -_infty^r fracpiepsilon_ fracqr^ddr fracpiepsilon_ fracqr Für den Bereich r R gilt hingegen: Phir -_infty^r vecE ddvecr -_infty^R fracpiepsilon_ fracqr^ddr-_R^r ddr fracpiepsilon_ fracqR abc Die Formel um die elektrostatische Energie zu berechnen lautet: tcbhighmathaufgabeW fracepsilon_ _^infty vecE^ ddx^ In diesem Fall führt das zu: W piepsilon_ frac_^infty E^r^ ddvecr piepsilon__^inftyfracpi^epsilon_^ fracr^r^ddr fracq^piepsilon_left_^R ddr+_r^inftyfracr^ddr fracq^piepsilon_R Dieser Ausdruck divergiert für Rrightarrow . abcliste
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Original exercise: Homogen geladene Kugel by rk ( | | )