Faraday's Law
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:
The magnetic flux through a loop of wire is given by the function Phi_mt. Determine a formal expression for the induced emf as a function of time resulting from the fluxes in a to c and find the units of the respective parameters. Graph the flux and the induced emf. abcliste abc Phi_mt Phi_left-leftfractt_-right^right abc Phi_mt Phi_sinomega t abc Phi_mt Phi_ e^-mut-t_^ abcliste
Solution:
abcliste abc mathcalEt -dotPhi_mt -Phi_ dvleft-leftfractt_-right^rightt +Phi_ leftfractt_-rightdvleftfractt_-rightt fracPhi_t_leftfractt_-right The units are: itemize item peak flux Phi_: Phi_uPhi item peak time t_: t_utp itemize includegraphicswidthcm#image_path:faraday-law-parabola-# abc mathcalEt -dotPhi_mt -Phi_ dvsinomega tt -Phi_ cosomega tdvomega tt -Phi_omegacosomega t The units are: itemize item peak flux Phi_: Phi_uPhi item angular frequency omega: omegauom itemize includegraphicswidthcm#image_path:faraday-law-sinusoidal-# abc mathcalEt -dotPhi_mt -Phi_ dvlefte^-mut-t_^rightt -Phi_ e^-mut-t_^ dvleft-mut-t_^rightt +mut-t_Phi_ e^-mut-t_^ dvt-t_t muPhi_ t-t_ e^-mut-t_^ The induced emf has extremal pos for dotmathcalEt: dotmathcalEt mu Phi_leftdvt-t_t e^-mut-t_^+t-t_dvlefte^-mut-t_^righttright muPhi_lefte^-mut-t_^+t-t_ e^-mut-t_^ left-mut-t_rightright muPhi_ e^-mut-t_^left-mut-t_^right This expression is equal to for t-t_ pmfracsqrtmu The extrema are therefore mathcalEpmfracsqrtmu pm muPhi_fracsqrtmu e^-mufracmu pmPhi_sqrtmu e^-frac pmPhi_sqrtfracmue The units are: itemize item peak flux Phi_: Phi_uPhi item peak time t_: t_utp item width parameter mu: muumu itemize includegraphicswidthcm#image_path:faraday-law-gauss# abcliste
The magnetic flux through a loop of wire is given by the function Phi_mt. Determine a formal expression for the induced emf as a function of time resulting from the fluxes in a to c and find the units of the respective parameters. Graph the flux and the induced emf. abcliste abc Phi_mt Phi_left-leftfractt_-right^right abc Phi_mt Phi_sinomega t abc Phi_mt Phi_ e^-mut-t_^ abcliste
Solution:
abcliste abc mathcalEt -dotPhi_mt -Phi_ dvleft-leftfractt_-right^rightt +Phi_ leftfractt_-rightdvleftfractt_-rightt fracPhi_t_leftfractt_-right The units are: itemize item peak flux Phi_: Phi_uPhi item peak time t_: t_utp itemize includegraphicswidthcm#image_path:faraday-law-parabola-# abc mathcalEt -dotPhi_mt -Phi_ dvsinomega tt -Phi_ cosomega tdvomega tt -Phi_omegacosomega t The units are: itemize item peak flux Phi_: Phi_uPhi item angular frequency omega: omegauom itemize includegraphicswidthcm#image_path:faraday-law-sinusoidal-# abc mathcalEt -dotPhi_mt -Phi_ dvlefte^-mut-t_^rightt -Phi_ e^-mut-t_^ dvleft-mut-t_^rightt +mut-t_Phi_ e^-mut-t_^ dvt-t_t muPhi_ t-t_ e^-mut-t_^ The induced emf has extremal pos for dotmathcalEt: dotmathcalEt mu Phi_leftdvt-t_t e^-mut-t_^+t-t_dvlefte^-mut-t_^righttright muPhi_lefte^-mut-t_^+t-t_ e^-mut-t_^ left-mut-t_rightright muPhi_ e^-mut-t_^left-mut-t_^right This expression is equal to for t-t_ pmfracsqrtmu The extrema are therefore mathcalEpmfracsqrtmu pm muPhi_fracsqrtmu e^-mufracmu pmPhi_sqrtmu e^-frac pmPhi_sqrtfracmue The units are: itemize item peak flux Phi_: Phi_uPhi item peak time t_: t_utp item width parameter mu: muumu itemize includegraphicswidthcm#image_path:faraday-law-gauss# abcliste
Meta Information
Exercise:
The magnetic flux through a loop of wire is given by the function Phi_mt. Determine a formal expression for the induced emf as a function of time resulting from the fluxes in a to c and find the units of the respective parameters. Graph the flux and the induced emf. abcliste abc Phi_mt Phi_left-leftfractt_-right^right abc Phi_mt Phi_sinomega t abc Phi_mt Phi_ e^-mut-t_^ abcliste
Solution:
abcliste abc mathcalEt -dotPhi_mt -Phi_ dvleft-leftfractt_-right^rightt +Phi_ leftfractt_-rightdvleftfractt_-rightt fracPhi_t_leftfractt_-right The units are: itemize item peak flux Phi_: Phi_uPhi item peak time t_: t_utp itemize includegraphicswidthcm#image_path:faraday-law-parabola-# abc mathcalEt -dotPhi_mt -Phi_ dvsinomega tt -Phi_ cosomega tdvomega tt -Phi_omegacosomega t The units are: itemize item peak flux Phi_: Phi_uPhi item angular frequency omega: omegauom itemize includegraphicswidthcm#image_path:faraday-law-sinusoidal-# abc mathcalEt -dotPhi_mt -Phi_ dvlefte^-mut-t_^rightt -Phi_ e^-mut-t_^ dvleft-mut-t_^rightt +mut-t_Phi_ e^-mut-t_^ dvt-t_t muPhi_ t-t_ e^-mut-t_^ The induced emf has extremal pos for dotmathcalEt: dotmathcalEt mu Phi_leftdvt-t_t e^-mut-t_^+t-t_dvlefte^-mut-t_^righttright muPhi_lefte^-mut-t_^+t-t_ e^-mut-t_^ left-mut-t_rightright muPhi_ e^-mut-t_^left-mut-t_^right This expression is equal to for t-t_ pmfracsqrtmu The extrema are therefore mathcalEpmfracsqrtmu pm muPhi_fracsqrtmu e^-mufracmu pmPhi_sqrtmu e^-frac pmPhi_sqrtfracmue The units are: itemize item peak flux Phi_: Phi_uPhi item peak time t_: t_utp item width parameter mu: muumu itemize includegraphicswidthcm#image_path:faraday-law-gauss# abcliste
The magnetic flux through a loop of wire is given by the function Phi_mt. Determine a formal expression for the induced emf as a function of time resulting from the fluxes in a to c and find the units of the respective parameters. Graph the flux and the induced emf. abcliste abc Phi_mt Phi_left-leftfractt_-right^right abc Phi_mt Phi_sinomega t abc Phi_mt Phi_ e^-mut-t_^ abcliste
Solution:
abcliste abc mathcalEt -dotPhi_mt -Phi_ dvleft-leftfractt_-right^rightt +Phi_ leftfractt_-rightdvleftfractt_-rightt fracPhi_t_leftfractt_-right The units are: itemize item peak flux Phi_: Phi_uPhi item peak time t_: t_utp itemize includegraphicswidthcm#image_path:faraday-law-parabola-# abc mathcalEt -dotPhi_mt -Phi_ dvsinomega tt -Phi_ cosomega tdvomega tt -Phi_omegacosomega t The units are: itemize item peak flux Phi_: Phi_uPhi item angular frequency omega: omegauom itemize includegraphicswidthcm#image_path:faraday-law-sinusoidal-# abc mathcalEt -dotPhi_mt -Phi_ dvlefte^-mut-t_^rightt -Phi_ e^-mut-t_^ dvleft-mut-t_^rightt +mut-t_Phi_ e^-mut-t_^ dvt-t_t muPhi_ t-t_ e^-mut-t_^ The induced emf has extremal pos for dotmathcalEt: dotmathcalEt mu Phi_leftdvt-t_t e^-mut-t_^+t-t_dvlefte^-mut-t_^righttright muPhi_lefte^-mut-t_^+t-t_ e^-mut-t_^ left-mut-t_rightright muPhi_ e^-mut-t_^left-mut-t_^right This expression is equal to for t-t_ pmfracsqrtmu The extrema are therefore mathcalEpmfracsqrtmu pm muPhi_fracsqrtmu e^-mufracmu pmPhi_sqrtmu e^-frac pmPhi_sqrtfracmue The units are: itemize item peak flux Phi_: Phi_uPhi item peak time t_: t_utp item width parameter mu: muumu itemize includegraphicswidthcm#image_path:faraday-law-gauss# abcliste
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