Numerical Calculation of Magnetic Flux
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:
Write computer programs to calculate the magnetic flux for the following two situations: abcliste abc The flux of a magnetic field in the z-direction through a square plate with sides a in the xy-plane centre at the origin. The strength of the magnetic field is given by the expression Bx yB_left-fracx^+y^a^right abc The flux of a magnetic field through a surface defined by the function zx yssczmaxleft-leftfrac xaright^right This surface corresponds to a parabola in the xz-plane that is extruded along the y-axis. The surface is limited by the conditions xin -a/ a/ and yin -L/ L/ i.e. it has a width a and a length L. medskip The magnetic field is given by the expression vecB pmatrixalpha xB_ e^-beta z pmatrix The x-component linearly increases in the direction of the x-axis i.e. the vector is tilted with respect to the z-axis unless x. Its z-component has its reference value B_ on the xy-plane and it decreases exponentially along the positive z-axis. abcliste
Solution:
A commented Jupyter notebook with an example program is attached as a file.
Write computer programs to calculate the magnetic flux for the following two situations: abcliste abc The flux of a magnetic field in the z-direction through a square plate with sides a in the xy-plane centre at the origin. The strength of the magnetic field is given by the expression Bx yB_left-fracx^+y^a^right abc The flux of a magnetic field through a surface defined by the function zx yssczmaxleft-leftfrac xaright^right This surface corresponds to a parabola in the xz-plane that is extruded along the y-axis. The surface is limited by the conditions xin -a/ a/ and yin -L/ L/ i.e. it has a width a and a length L. medskip The magnetic field is given by the expression vecB pmatrixalpha xB_ e^-beta z pmatrix The x-component linearly increases in the direction of the x-axis i.e. the vector is tilted with respect to the z-axis unless x. Its z-component has its reference value B_ on the xy-plane and it decreases exponentially along the positive z-axis. abcliste
Solution:
A commented Jupyter notebook with an example program is attached as a file.
Meta Information
Exercise:
Write computer programs to calculate the magnetic flux for the following two situations: abcliste abc The flux of a magnetic field in the z-direction through a square plate with sides a in the xy-plane centre at the origin. The strength of the magnetic field is given by the expression Bx yB_left-fracx^+y^a^right abc The flux of a magnetic field through a surface defined by the function zx yssczmaxleft-leftfrac xaright^right This surface corresponds to a parabola in the xz-plane that is extruded along the y-axis. The surface is limited by the conditions xin -a/ a/ and yin -L/ L/ i.e. it has a width a and a length L. medskip The magnetic field is given by the expression vecB pmatrixalpha xB_ e^-beta z pmatrix The x-component linearly increases in the direction of the x-axis i.e. the vector is tilted with respect to the z-axis unless x. Its z-component has its reference value B_ on the xy-plane and it decreases exponentially along the positive z-axis. abcliste
Solution:
A commented Jupyter notebook with an example program is attached as a file.
Write computer programs to calculate the magnetic flux for the following two situations: abcliste abc The flux of a magnetic field in the z-direction through a square plate with sides a in the xy-plane centre at the origin. The strength of the magnetic field is given by the expression Bx yB_left-fracx^+y^a^right abc The flux of a magnetic field through a surface defined by the function zx yssczmaxleft-leftfrac xaright^right This surface corresponds to a parabola in the xz-plane that is extruded along the y-axis. The surface is limited by the conditions xin -a/ a/ and yin -L/ L/ i.e. it has a width a and a length L. medskip The magnetic field is given by the expression vecB pmatrixalpha xB_ e^-beta z pmatrix The x-component linearly increases in the direction of the x-axis i.e. the vector is tilted with respect to the z-axis unless x. Its z-component has its reference value B_ on the xy-plane and it decreases exponentially along the positive z-axis. abcliste
Solution:
A commented Jupyter notebook with an example program is attached as a file.
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