Poynting Vector
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:
The amplitude of the magnetic field vector of an electromagnetic wave propagating along the z axis is vec B pmatrix B_x B_y pmatrix Express the amplitude of the corresponding electric field vector and the Poynting vector in terms of B_x B_y and the speed of light.
Solution:
The electric field vector is vec E vec Bcross vec c pmatrix B_x B_y pmatrix cross pmatrix c pmatrix pmatrix B_yc- -B_xc - pmatrix cpmatrix B_y -B_x pmatrix The two field vectors are perpicular to each other: vec E vec B c pmatrix B_y -B_x pmatrix pmatrix B_x B_y pmatrix cB_yB_x-B_xB_y The amplitude of the Poynting vector is vec S_ fracmu_vec Ecrossvec B fraccmu_pmatrix B_y -B_x pmatrix cross pmatrix B_x B_y pmatrix fraccmu_pmatrix B_yB_y--B_xB_x pmatrix fraccmu_ pmatrix B_y^+B_x^ pmatrix fraccmu_ pmatrix B_^ pmatrix As expected the Poynting vector has the same direction as the direction of propagation. Its amplitude is equal to S_ fracc B_^mu_ fracmu_rE_ B_
The amplitude of the magnetic field vector of an electromagnetic wave propagating along the z axis is vec B pmatrix B_x B_y pmatrix Express the amplitude of the corresponding electric field vector and the Poynting vector in terms of B_x B_y and the speed of light.
Solution:
The electric field vector is vec E vec Bcross vec c pmatrix B_x B_y pmatrix cross pmatrix c pmatrix pmatrix B_yc- -B_xc - pmatrix cpmatrix B_y -B_x pmatrix The two field vectors are perpicular to each other: vec E vec B c pmatrix B_y -B_x pmatrix pmatrix B_x B_y pmatrix cB_yB_x-B_xB_y The amplitude of the Poynting vector is vec S_ fracmu_vec Ecrossvec B fraccmu_pmatrix B_y -B_x pmatrix cross pmatrix B_x B_y pmatrix fraccmu_pmatrix B_yB_y--B_xB_x pmatrix fraccmu_ pmatrix B_y^+B_x^ pmatrix fraccmu_ pmatrix B_^ pmatrix As expected the Poynting vector has the same direction as the direction of propagation. Its amplitude is equal to S_ fracc B_^mu_ fracmu_rE_ B_
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Exercise:
The amplitude of the magnetic field vector of an electromagnetic wave propagating along the z axis is vec B pmatrix B_x B_y pmatrix Express the amplitude of the corresponding electric field vector and the Poynting vector in terms of B_x B_y and the speed of light.
Solution:
The electric field vector is vec E vec Bcross vec c pmatrix B_x B_y pmatrix cross pmatrix c pmatrix pmatrix B_yc- -B_xc - pmatrix cpmatrix B_y -B_x pmatrix The two field vectors are perpicular to each other: vec E vec B c pmatrix B_y -B_x pmatrix pmatrix B_x B_y pmatrix cB_yB_x-B_xB_y The amplitude of the Poynting vector is vec S_ fracmu_vec Ecrossvec B fraccmu_pmatrix B_y -B_x pmatrix cross pmatrix B_x B_y pmatrix fraccmu_pmatrix B_yB_y--B_xB_x pmatrix fraccmu_ pmatrix B_y^+B_x^ pmatrix fraccmu_ pmatrix B_^ pmatrix As expected the Poynting vector has the same direction as the direction of propagation. Its amplitude is equal to S_ fracc B_^mu_ fracmu_rE_ B_
The amplitude of the magnetic field vector of an electromagnetic wave propagating along the z axis is vec B pmatrix B_x B_y pmatrix Express the amplitude of the corresponding electric field vector and the Poynting vector in terms of B_x B_y and the speed of light.
Solution:
The electric field vector is vec E vec Bcross vec c pmatrix B_x B_y pmatrix cross pmatrix c pmatrix pmatrix B_yc- -B_xc - pmatrix cpmatrix B_y -B_x pmatrix The two field vectors are perpicular to each other: vec E vec B c pmatrix B_y -B_x pmatrix pmatrix B_x B_y pmatrix cB_yB_x-B_xB_y The amplitude of the Poynting vector is vec S_ fracmu_vec Ecrossvec B fraccmu_pmatrix B_y -B_x pmatrix cross pmatrix B_x B_y pmatrix fraccmu_pmatrix B_yB_y--B_xB_x pmatrix fraccmu_ pmatrix B_y^+B_x^ pmatrix fraccmu_ pmatrix B_^ pmatrix As expected the Poynting vector has the same direction as the direction of propagation. Its amplitude is equal to S_ fracc B_^mu_ fracmu_rE_ B_
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