Wien-Filter (relativistisch)
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
Short
Video
\(\LaTeX\)
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Exercise:
Teilchen mit der Ladung q -e durchlaufen zunächst ein Wienfilter mit E^siV/m und B.simT und treten dann in einen Raumbereich ein in dem nur noch dieses Magnetfeld herrscht s. Skizze unten. Hier beschreiben die Teilchen dann eine Kreisbahn mit dem Radius .sicm. enumerate item Wie gross ist die Geschwindigkeit der Teilchen die das Wienfilter passieren in Prozent der Lichtgeschwindigkeit? item Berechnen Sie die Ruhemasse m_ dieser Teilchen. Um welche Teilchen könnte es sich handeln? enumerate center tikzpicturelatexscale. %draw step.colorgray! -- grid ; %fill circle .; drawthickdecoration markings markat position . with arrow postactiondecorate -.--.; draw .rectangle-.; draw -.rectangle-.-; draw .rectangle.; draw -.rectangle.-; draw line width.mm ..--..; draw line width.mm .-.--.-.; draw very thick ..--..; draw very thick .-.--.-.; draw .. circle .; draw .-. circle .; foreach x in ...... foreach y in -.. node at xy otimes; draw .. rectangle ..node abovexshift-.cm scriptsizeSchirm; draw thick . arc ::-; foreach x in foreach y in -...... node at xy otimes; node at .. boldsymbol+; node at .-. boldsymbol-; tikzpicture center
Solution:
enumerate item Für das Wienfilter gilt: F_mathrmelF_mathrmLRa qvBqE Ra vfracEB.^sim/s Das sind % der Lichtgeschwindigkeit. item Aufgrund des Resultates in Teilaufgabe a müssen wir relativistisch rechnen: F_mathrmZF_mathrmLRa mfracv^rqvB Ra fracm_vr sqrt-fracv^c^qB Ra m_fracqrBsqrt-fracv^c^vres. ^-kg Das entspricht der Masse von Elektronen. enumerate
Teilchen mit der Ladung q -e durchlaufen zunächst ein Wienfilter mit E^siV/m und B.simT und treten dann in einen Raumbereich ein in dem nur noch dieses Magnetfeld herrscht s. Skizze unten. Hier beschreiben die Teilchen dann eine Kreisbahn mit dem Radius .sicm. enumerate item Wie gross ist die Geschwindigkeit der Teilchen die das Wienfilter passieren in Prozent der Lichtgeschwindigkeit? item Berechnen Sie die Ruhemasse m_ dieser Teilchen. Um welche Teilchen könnte es sich handeln? enumerate center tikzpicturelatexscale. %draw step.colorgray! -- grid ; %fill circle .; drawthickdecoration markings markat position . with arrow postactiondecorate -.--.; draw .rectangle-.; draw -.rectangle-.-; draw .rectangle.; draw -.rectangle.-; draw line width.mm ..--..; draw line width.mm .-.--.-.; draw very thick ..--..; draw very thick .-.--.-.; draw .. circle .; draw .-. circle .; foreach x in ...... foreach y in -.. node at xy otimes; draw .. rectangle ..node abovexshift-.cm scriptsizeSchirm; draw thick . arc ::-; foreach x in foreach y in -...... node at xy otimes; node at .. boldsymbol+; node at .-. boldsymbol-; tikzpicture center
Solution:
enumerate item Für das Wienfilter gilt: F_mathrmelF_mathrmLRa qvBqE Ra vfracEB.^sim/s Das sind % der Lichtgeschwindigkeit. item Aufgrund des Resultates in Teilaufgabe a müssen wir relativistisch rechnen: F_mathrmZF_mathrmLRa mfracv^rqvB Ra fracm_vr sqrt-fracv^c^qB Ra m_fracqrBsqrt-fracv^c^vres. ^-kg Das entspricht der Masse von Elektronen. enumerate
Meta Information
Exercise:
Teilchen mit der Ladung q -e durchlaufen zunächst ein Wienfilter mit E^siV/m und B.simT und treten dann in einen Raumbereich ein in dem nur noch dieses Magnetfeld herrscht s. Skizze unten. Hier beschreiben die Teilchen dann eine Kreisbahn mit dem Radius .sicm. enumerate item Wie gross ist die Geschwindigkeit der Teilchen die das Wienfilter passieren in Prozent der Lichtgeschwindigkeit? item Berechnen Sie die Ruhemasse m_ dieser Teilchen. Um welche Teilchen könnte es sich handeln? enumerate center tikzpicturelatexscale. %draw step.colorgray! -- grid ; %fill circle .; drawthickdecoration markings markat position . with arrow postactiondecorate -.--.; draw .rectangle-.; draw -.rectangle-.-; draw .rectangle.; draw -.rectangle.-; draw line width.mm ..--..; draw line width.mm .-.--.-.; draw very thick ..--..; draw very thick .-.--.-.; draw .. circle .; draw .-. circle .; foreach x in ...... foreach y in -.. node at xy otimes; draw .. rectangle ..node abovexshift-.cm scriptsizeSchirm; draw thick . arc ::-; foreach x in foreach y in -...... node at xy otimes; node at .. boldsymbol+; node at .-. boldsymbol-; tikzpicture center
Solution:
enumerate item Für das Wienfilter gilt: F_mathrmelF_mathrmLRa qvBqE Ra vfracEB.^sim/s Das sind % der Lichtgeschwindigkeit. item Aufgrund des Resultates in Teilaufgabe a müssen wir relativistisch rechnen: F_mathrmZF_mathrmLRa mfracv^rqvB Ra fracm_vr sqrt-fracv^c^qB Ra m_fracqrBsqrt-fracv^c^vres. ^-kg Das entspricht der Masse von Elektronen. enumerate
Teilchen mit der Ladung q -e durchlaufen zunächst ein Wienfilter mit E^siV/m und B.simT und treten dann in einen Raumbereich ein in dem nur noch dieses Magnetfeld herrscht s. Skizze unten. Hier beschreiben die Teilchen dann eine Kreisbahn mit dem Radius .sicm. enumerate item Wie gross ist die Geschwindigkeit der Teilchen die das Wienfilter passieren in Prozent der Lichtgeschwindigkeit? item Berechnen Sie die Ruhemasse m_ dieser Teilchen. Um welche Teilchen könnte es sich handeln? enumerate center tikzpicturelatexscale. %draw step.colorgray! -- grid ; %fill circle .; drawthickdecoration markings markat position . with arrow postactiondecorate -.--.; draw .rectangle-.; draw -.rectangle-.-; draw .rectangle.; draw -.rectangle.-; draw line width.mm ..--..; draw line width.mm .-.--.-.; draw very thick ..--..; draw very thick .-.--.-.; draw .. circle .; draw .-. circle .; foreach x in ...... foreach y in -.. node at xy otimes; draw .. rectangle ..node abovexshift-.cm scriptsizeSchirm; draw thick . arc ::-; foreach x in foreach y in -...... node at xy otimes; node at .. boldsymbol+; node at .-. boldsymbol-; tikzpicture center
Solution:
enumerate item Für das Wienfilter gilt: F_mathrmelF_mathrmLRa qvBqE Ra vfracEB.^sim/s Das sind % der Lichtgeschwindigkeit. item Aufgrund des Resultates in Teilaufgabe a müssen wir relativistisch rechnen: F_mathrmZF_mathrmLRa mfracv^rqvB Ra fracm_vr sqrt-fracv^c^qB Ra m_fracqrBsqrt-fracv^c^vres. ^-kg Das entspricht der Masse von Elektronen. enumerate
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