Drei Ladungen im Dreieck
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:
In einem rechtwinkligen gleichschenkligen Dreieck sind drei Ladungen so verteilt dass die Ladung am rechten Winkel q_ muC und die beiden anderen q_ muC und q_ muC sind. center tikzpicture % Dreieick draw thick -- node below footnotesize.centim++ -- node rightfootnotesizecentim++ -.. -- node leftfootnotesizecentim++ -.-.; % Ladungen draw fillred circle mm node leftxshift-mm q_; draw fillred circle mm node rightxshiftmm q_; draw fillred .. circle mm node aboveyshiftmm q_; tikzpicture center Bestimmen Sie die resultiere Kraft auf q_ und die Richtung relativ zur Horizontalen.
Solution:
Die einzelnen Kräfte werden wie folgt berechnet: F_i fracpivarepsilon_fracq_q_ir^ wobei r .m und q_i muC resp. muC sind q_ muC. Damit erhalten wir für F_ apx N und für F_ apx N. Da diese beiden Kräfte bereits rechtwinklig aufeinander stehen können wir direkt die resultiere Kraft bestimmen. Es gilt: F_textres sqrtF_^+F_^ apx N. Die Richtung ist etwas umständlich da wir ein gedrehtes Koordinatensystem haben erhalten wir mit tan alpha fracF_F_ myRarrow alpha apx grad nur den Winkel bezüglich F_. Daher ist der Winkel zur Horizontalen um grad grösser. Damit erhalten wir also: alpha' grad
In einem rechtwinkligen gleichschenkligen Dreieck sind drei Ladungen so verteilt dass die Ladung am rechten Winkel q_ muC und die beiden anderen q_ muC und q_ muC sind. center tikzpicture % Dreieick draw thick -- node below footnotesize.centim++ -- node rightfootnotesizecentim++ -.. -- node leftfootnotesizecentim++ -.-.; % Ladungen draw fillred circle mm node leftxshift-mm q_; draw fillred circle mm node rightxshiftmm q_; draw fillred .. circle mm node aboveyshiftmm q_; tikzpicture center Bestimmen Sie die resultiere Kraft auf q_ und die Richtung relativ zur Horizontalen.
Solution:
Die einzelnen Kräfte werden wie folgt berechnet: F_i fracpivarepsilon_fracq_q_ir^ wobei r .m und q_i muC resp. muC sind q_ muC. Damit erhalten wir für F_ apx N und für F_ apx N. Da diese beiden Kräfte bereits rechtwinklig aufeinander stehen können wir direkt die resultiere Kraft bestimmen. Es gilt: F_textres sqrtF_^+F_^ apx N. Die Richtung ist etwas umständlich da wir ein gedrehtes Koordinatensystem haben erhalten wir mit tan alpha fracF_F_ myRarrow alpha apx grad nur den Winkel bezüglich F_. Daher ist der Winkel zur Horizontalen um grad grösser. Damit erhalten wir also: alpha' grad
Meta Information
Exercise:
In einem rechtwinkligen gleichschenkligen Dreieck sind drei Ladungen so verteilt dass die Ladung am rechten Winkel q_ muC und die beiden anderen q_ muC und q_ muC sind. center tikzpicture % Dreieick draw thick -- node below footnotesize.centim++ -- node rightfootnotesizecentim++ -.. -- node leftfootnotesizecentim++ -.-.; % Ladungen draw fillred circle mm node leftxshift-mm q_; draw fillred circle mm node rightxshiftmm q_; draw fillred .. circle mm node aboveyshiftmm q_; tikzpicture center Bestimmen Sie die resultiere Kraft auf q_ und die Richtung relativ zur Horizontalen.
Solution:
Die einzelnen Kräfte werden wie folgt berechnet: F_i fracpivarepsilon_fracq_q_ir^ wobei r .m und q_i muC resp. muC sind q_ muC. Damit erhalten wir für F_ apx N und für F_ apx N. Da diese beiden Kräfte bereits rechtwinklig aufeinander stehen können wir direkt die resultiere Kraft bestimmen. Es gilt: F_textres sqrtF_^+F_^ apx N. Die Richtung ist etwas umständlich da wir ein gedrehtes Koordinatensystem haben erhalten wir mit tan alpha fracF_F_ myRarrow alpha apx grad nur den Winkel bezüglich F_. Daher ist der Winkel zur Horizontalen um grad grösser. Damit erhalten wir also: alpha' grad
In einem rechtwinkligen gleichschenkligen Dreieck sind drei Ladungen so verteilt dass die Ladung am rechten Winkel q_ muC und die beiden anderen q_ muC und q_ muC sind. center tikzpicture % Dreieick draw thick -- node below footnotesize.centim++ -- node rightfootnotesizecentim++ -.. -- node leftfootnotesizecentim++ -.-.; % Ladungen draw fillred circle mm node leftxshift-mm q_; draw fillred circle mm node rightxshiftmm q_; draw fillred .. circle mm node aboveyshiftmm q_; tikzpicture center Bestimmen Sie die resultiere Kraft auf q_ und die Richtung relativ zur Horizontalen.
Solution:
Die einzelnen Kräfte werden wie folgt berechnet: F_i fracpivarepsilon_fracq_q_ir^ wobei r .m und q_i muC resp. muC sind q_ muC. Damit erhalten wir für F_ apx N und für F_ apx N. Da diese beiden Kräfte bereits rechtwinklig aufeinander stehen können wir direkt die resultiere Kraft bestimmen. Es gilt: F_textres sqrtF_^+F_^ apx N. Die Richtung ist etwas umständlich da wir ein gedrehtes Koordinatensystem haben erhalten wir mit tan alpha fracF_F_ myRarrow alpha apx grad nur den Winkel bezüglich F_. Daher ist der Winkel zur Horizontalen um grad grösser. Damit erhalten wir also: alpha' grad
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