Elektrostatik: Coulombkraft 9
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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Video
\(\LaTeX\)
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Exercise:
Drei Punktladungen befinden sich auf den Ecken eines Quadrats mit Kantenlänge a siehe Abb.reffig:QpQpQnQuadrat. Es sei Q_Q_-Q_. Die Ladungen Q_ und Q_ bilden einen Dipol der Länge a. Sei F die Kraft von Q_ auf Q_. % . Sept. Lie. a Berechnen Sie F für Q_.sipC und asitextensuremathupmu m. b Bestimmen Sie Betrag und Richtung der resultieren Kraft F_res von Q_ auf den Dipol. Rechnen Sie rein formal und drücken Sie F_res als Vielfaches von F aus. figureH includegraphicswidthtextwidth#image_path:QpQpQnQuadrat# caption labelfig:QpQpQnQuadrat figure
Solution:
% . Sept. Lie. * &texta Ffracpivarepsilon_fracQ_Q_a^ fracpi .eesiAs/Vm leftfrac.eesiC eesim right^ uuline.sitextensuremathupmu N &textb Siehe Abbildung reffig:QpQpQnQuadratKraft. &quad F_ F/ textquad da quad r_a sqrt textquad undquad Fpropto /r^ &textquad Kosinussatz: F_res sqrtF^+F/^-F^cosbeta Fsqrttfrac-cos sidegree approx . F &textquad Sinussatz: alpha arcsinleft fracF_sinbetaF_res right arcsinleft fracsinsidegreesqrttfrac-cos sidegree right approx .sidegree * centerline minipage.textwidth centering includegraphicsscale.Grafiken/QpQpQnQuadrat/QpQpQnQuadratKraft.pdf captlabelfig:QpQpQnQuadratKraft Kräfte auf den Dipol minipage newpage figureH includegraphicswidthtextwidth#image_path:QpQpQnQuadrat# caption labelfig:QpQpQnQuadrat figure figureH includegraphicswidthtextwidth#image_path:QpQpQnQuadratKraft# caption labelfig:QpQpQnQuadrat figure
Drei Punktladungen befinden sich auf den Ecken eines Quadrats mit Kantenlänge a siehe Abb.reffig:QpQpQnQuadrat. Es sei Q_Q_-Q_. Die Ladungen Q_ und Q_ bilden einen Dipol der Länge a. Sei F die Kraft von Q_ auf Q_. % . Sept. Lie. a Berechnen Sie F für Q_.sipC und asitextensuremathupmu m. b Bestimmen Sie Betrag und Richtung der resultieren Kraft F_res von Q_ auf den Dipol. Rechnen Sie rein formal und drücken Sie F_res als Vielfaches von F aus. figureH includegraphicswidthtextwidth#image_path:QpQpQnQuadrat# caption labelfig:QpQpQnQuadrat figure
Solution:
% . Sept. Lie. * &texta Ffracpivarepsilon_fracQ_Q_a^ fracpi .eesiAs/Vm leftfrac.eesiC eesim right^ uuline.sitextensuremathupmu N &textb Siehe Abbildung reffig:QpQpQnQuadratKraft. &quad F_ F/ textquad da quad r_a sqrt textquad undquad Fpropto /r^ &textquad Kosinussatz: F_res sqrtF^+F/^-F^cosbeta Fsqrttfrac-cos sidegree approx . F &textquad Sinussatz: alpha arcsinleft fracF_sinbetaF_res right arcsinleft fracsinsidegreesqrttfrac-cos sidegree right approx .sidegree * centerline minipage.textwidth centering includegraphicsscale.Grafiken/QpQpQnQuadrat/QpQpQnQuadratKraft.pdf captlabelfig:QpQpQnQuadratKraft Kräfte auf den Dipol minipage newpage figureH includegraphicswidthtextwidth#image_path:QpQpQnQuadrat# caption labelfig:QpQpQnQuadrat figure figureH includegraphicswidthtextwidth#image_path:QpQpQnQuadratKraft# caption labelfig:QpQpQnQuadrat figure
Meta Information
Exercise:
Drei Punktladungen befinden sich auf den Ecken eines Quadrats mit Kantenlänge a siehe Abb.reffig:QpQpQnQuadrat. Es sei Q_Q_-Q_. Die Ladungen Q_ und Q_ bilden einen Dipol der Länge a. Sei F die Kraft von Q_ auf Q_. % . Sept. Lie. a Berechnen Sie F für Q_.sipC und asitextensuremathupmu m. b Bestimmen Sie Betrag und Richtung der resultieren Kraft F_res von Q_ auf den Dipol. Rechnen Sie rein formal und drücken Sie F_res als Vielfaches von F aus. figureH includegraphicswidthtextwidth#image_path:QpQpQnQuadrat# caption labelfig:QpQpQnQuadrat figure
Solution:
% . Sept. Lie. * &texta Ffracpivarepsilon_fracQ_Q_a^ fracpi .eesiAs/Vm leftfrac.eesiC eesim right^ uuline.sitextensuremathupmu N &textb Siehe Abbildung reffig:QpQpQnQuadratKraft. &quad F_ F/ textquad da quad r_a sqrt textquad undquad Fpropto /r^ &textquad Kosinussatz: F_res sqrtF^+F/^-F^cosbeta Fsqrttfrac-cos sidegree approx . F &textquad Sinussatz: alpha arcsinleft fracF_sinbetaF_res right arcsinleft fracsinsidegreesqrttfrac-cos sidegree right approx .sidegree * centerline minipage.textwidth centering includegraphicsscale.Grafiken/QpQpQnQuadrat/QpQpQnQuadratKraft.pdf captlabelfig:QpQpQnQuadratKraft Kräfte auf den Dipol minipage newpage figureH includegraphicswidthtextwidth#image_path:QpQpQnQuadrat# caption labelfig:QpQpQnQuadrat figure figureH includegraphicswidthtextwidth#image_path:QpQpQnQuadratKraft# caption labelfig:QpQpQnQuadrat figure
Drei Punktladungen befinden sich auf den Ecken eines Quadrats mit Kantenlänge a siehe Abb.reffig:QpQpQnQuadrat. Es sei Q_Q_-Q_. Die Ladungen Q_ und Q_ bilden einen Dipol der Länge a. Sei F die Kraft von Q_ auf Q_. % . Sept. Lie. a Berechnen Sie F für Q_.sipC und asitextensuremathupmu m. b Bestimmen Sie Betrag und Richtung der resultieren Kraft F_res von Q_ auf den Dipol. Rechnen Sie rein formal und drücken Sie F_res als Vielfaches von F aus. figureH includegraphicswidthtextwidth#image_path:QpQpQnQuadrat# caption labelfig:QpQpQnQuadrat figure
Solution:
% . Sept. Lie. * &texta Ffracpivarepsilon_fracQ_Q_a^ fracpi .eesiAs/Vm leftfrac.eesiC eesim right^ uuline.sitextensuremathupmu N &textb Siehe Abbildung reffig:QpQpQnQuadratKraft. &quad F_ F/ textquad da quad r_a sqrt textquad undquad Fpropto /r^ &textquad Kosinussatz: F_res sqrtF^+F/^-F^cosbeta Fsqrttfrac-cos sidegree approx . F &textquad Sinussatz: alpha arcsinleft fracF_sinbetaF_res right arcsinleft fracsinsidegreesqrttfrac-cos sidegree right approx .sidegree * centerline minipage.textwidth centering includegraphicsscale.Grafiken/QpQpQnQuadrat/QpQpQnQuadratKraft.pdf captlabelfig:QpQpQnQuadratKraft Kräfte auf den Dipol minipage newpage figureH includegraphicswidthtextwidth#image_path:QpQpQnQuadrat# caption labelfig:QpQpQnQuadrat figure figureH includegraphicswidthtextwidth#image_path:QpQpQnQuadratKraft# caption labelfig:QpQpQnQuadrat figure
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Elektrostatik: Coulombkraft by Lie