Field Vectors in Electromagnetic Waves
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 amplitudes of the electric and magnetic field vectors in an electromagnetic wave propagating along the x direction are vectors in the xy plane. abcliste abc For a magnetic field vector vecB pmatrix B_x B_y pmatrix find the components of the corresponding electric field vector. abc For an electric field vector vecE pmatrix E_x E_y pmatrix find the components of the corresponding magnetic field vector. abcliste
Solution:
abcliste abc The electric field vector is given by the relation vec E vec B cross vec c. It follows vec E pmatrix B_x B_y pmatrix cross pmatrix c pmatrix pmatrix B_y c - - B_x c B_x - B_y pmatrix pmatrix B_y c -B_x c pmatrix c pmatrix B_y -B_x pmatrix We can easily verify that vec E is perpicular to vec B and that E B c: vec E vec B B_x B_y + B_y -B_x B_x B_y - B_x B_y E absvec E sqrtE_x^ + E_y^ sqrtc B_y^+-c B_x^ sqrtc^ B_y^ + B_x^ c sqrtB_x^+B_y^ c absvec B c B abc abcliste
The amplitudes of the electric and magnetic field vectors in an electromagnetic wave propagating along the x direction are vectors in the xy plane. abcliste abc For a magnetic field vector vecB pmatrix B_x B_y pmatrix find the components of the corresponding electric field vector. abc For an electric field vector vecE pmatrix E_x E_y pmatrix find the components of the corresponding magnetic field vector. abcliste
Solution:
abcliste abc The electric field vector is given by the relation vec E vec B cross vec c. It follows vec E pmatrix B_x B_y pmatrix cross pmatrix c pmatrix pmatrix B_y c - - B_x c B_x - B_y pmatrix pmatrix B_y c -B_x c pmatrix c pmatrix B_y -B_x pmatrix We can easily verify that vec E is perpicular to vec B and that E B c: vec E vec B B_x B_y + B_y -B_x B_x B_y - B_x B_y E absvec E sqrtE_x^ + E_y^ sqrtc B_y^+-c B_x^ sqrtc^ B_y^ + B_x^ c sqrtB_x^+B_y^ c absvec B c B abc abcliste
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Exercise:
The amplitudes of the electric and magnetic field vectors in an electromagnetic wave propagating along the x direction are vectors in the xy plane. abcliste abc For a magnetic field vector vecB pmatrix B_x B_y pmatrix find the components of the corresponding electric field vector. abc For an electric field vector vecE pmatrix E_x E_y pmatrix find the components of the corresponding magnetic field vector. abcliste
Solution:
abcliste abc The electric field vector is given by the relation vec E vec B cross vec c. It follows vec E pmatrix B_x B_y pmatrix cross pmatrix c pmatrix pmatrix B_y c - - B_x c B_x - B_y pmatrix pmatrix B_y c -B_x c pmatrix c pmatrix B_y -B_x pmatrix We can easily verify that vec E is perpicular to vec B and that E B c: vec E vec B B_x B_y + B_y -B_x B_x B_y - B_x B_y E absvec E sqrtE_x^ + E_y^ sqrtc B_y^+-c B_x^ sqrtc^ B_y^ + B_x^ c sqrtB_x^+B_y^ c absvec B c B abc abcliste
The amplitudes of the electric and magnetic field vectors in an electromagnetic wave propagating along the x direction are vectors in the xy plane. abcliste abc For a magnetic field vector vecB pmatrix B_x B_y pmatrix find the components of the corresponding electric field vector. abc For an electric field vector vecE pmatrix E_x E_y pmatrix find the components of the corresponding magnetic field vector. abcliste
Solution:
abcliste abc The electric field vector is given by the relation vec E vec B cross vec c. It follows vec E pmatrix B_x B_y pmatrix cross pmatrix c pmatrix pmatrix B_y c - - B_x c B_x - B_y pmatrix pmatrix B_y c -B_x c pmatrix c pmatrix B_y -B_x pmatrix We can easily verify that vec E is perpicular to vec B and that E B c: vec E vec B B_x B_y + B_y -B_x B_x B_y - B_x B_y E absvec E sqrtE_x^ + E_y^ sqrtc B_y^+-c B_x^ sqrtc^ B_y^ + B_x^ c sqrtB_x^+B_y^ c absvec B c B abc abcliste
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