Dipole Field
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:
A dipole consists of two po charges pm q at a distance d. abclist abc Derive a formal expression for the field strength on the line connecting the two charges as a function of the position x measured from the center between the charges. What is the asymptotic behaviour for x gg d? abc Derive a formal expression for the field strength on the perpicular bisector of the segment connecting the two charges as a function of the position y on the bisector. What is the asymptotic behaviour for ygg d? abclist
Solution:
abclist abc The partial field vectors vecE_+ and vecE_- are displayed in the figure. center includegraphicswidth.mm#image_path:dipolfield-along-x# center The net field strength E is given by E E_- - E_+ k_C qleftfracx-d/^-fracx+d/^right k_C q fracx+d/^-x-d/^leftx^-d/^right^ k_C q fracx^+x d/+d/^-x^+x d/-d/^leftx^-d/^right^ k_C fracq x dleftx^-d/^right^ For xgg d all mands but the leading term x^ are negligible in the denominator. The field strength is approximately equal to E &approx k_C fracq x dx^ k_C fracq dx^ abc The figure shows how the net electric field vector E deps on the partial field vectors E_+ and E_-. center includegraphicswidthmm#image_path:dipolfield-along-y# center Using similar triangles it follows fracEE_+ fracdr rightarrow E E_+fracdr k_C fracqr^fracdrk_C fracq dr^ k_C fracq dleftd/^+y^right^/ For ygg d the term in d can be neglected in the denominator. The field strength is approximately equal to E &approx k_Cfracq dy^^/ k_Cfracq dy^ abclist It turns out that the field strength of a dipole decreases like /r^ for rgg d. This is different from the behaviour of a single po charge where the field drops off like /r^ inverse square law.
A dipole consists of two po charges pm q at a distance d. abclist abc Derive a formal expression for the field strength on the line connecting the two charges as a function of the position x measured from the center between the charges. What is the asymptotic behaviour for x gg d? abc Derive a formal expression for the field strength on the perpicular bisector of the segment connecting the two charges as a function of the position y on the bisector. What is the asymptotic behaviour for ygg d? abclist
Solution:
abclist abc The partial field vectors vecE_+ and vecE_- are displayed in the figure. center includegraphicswidth.mm#image_path:dipolfield-along-x# center The net field strength E is given by E E_- - E_+ k_C qleftfracx-d/^-fracx+d/^right k_C q fracx+d/^-x-d/^leftx^-d/^right^ k_C q fracx^+x d/+d/^-x^+x d/-d/^leftx^-d/^right^ k_C fracq x dleftx^-d/^right^ For xgg d all mands but the leading term x^ are negligible in the denominator. The field strength is approximately equal to E &approx k_C fracq x dx^ k_C fracq dx^ abc The figure shows how the net electric field vector E deps on the partial field vectors E_+ and E_-. center includegraphicswidthmm#image_path:dipolfield-along-y# center Using similar triangles it follows fracEE_+ fracdr rightarrow E E_+fracdr k_C fracqr^fracdrk_C fracq dr^ k_C fracq dleftd/^+y^right^/ For ygg d the term in d can be neglected in the denominator. The field strength is approximately equal to E &approx k_Cfracq dy^^/ k_Cfracq dy^ abclist It turns out that the field strength of a dipole decreases like /r^ for rgg d. This is different from the behaviour of a single po charge where the field drops off like /r^ inverse square law.
Meta Information
Exercise:
A dipole consists of two po charges pm q at a distance d. abclist abc Derive a formal expression for the field strength on the line connecting the two charges as a function of the position x measured from the center between the charges. What is the asymptotic behaviour for x gg d? abc Derive a formal expression for the field strength on the perpicular bisector of the segment connecting the two charges as a function of the position y on the bisector. What is the asymptotic behaviour for ygg d? abclist
Solution:
abclist abc The partial field vectors vecE_+ and vecE_- are displayed in the figure. center includegraphicswidth.mm#image_path:dipolfield-along-x# center The net field strength E is given by E E_- - E_+ k_C qleftfracx-d/^-fracx+d/^right k_C q fracx+d/^-x-d/^leftx^-d/^right^ k_C q fracx^+x d/+d/^-x^+x d/-d/^leftx^-d/^right^ k_C fracq x dleftx^-d/^right^ For xgg d all mands but the leading term x^ are negligible in the denominator. The field strength is approximately equal to E &approx k_C fracq x dx^ k_C fracq dx^ abc The figure shows how the net electric field vector E deps on the partial field vectors E_+ and E_-. center includegraphicswidthmm#image_path:dipolfield-along-y# center Using similar triangles it follows fracEE_+ fracdr rightarrow E E_+fracdr k_C fracqr^fracdrk_C fracq dr^ k_C fracq dleftd/^+y^right^/ For ygg d the term in d can be neglected in the denominator. The field strength is approximately equal to E &approx k_Cfracq dy^^/ k_Cfracq dy^ abclist It turns out that the field strength of a dipole decreases like /r^ for rgg d. This is different from the behaviour of a single po charge where the field drops off like /r^ inverse square law.
A dipole consists of two po charges pm q at a distance d. abclist abc Derive a formal expression for the field strength on the line connecting the two charges as a function of the position x measured from the center between the charges. What is the asymptotic behaviour for x gg d? abc Derive a formal expression for the field strength on the perpicular bisector of the segment connecting the two charges as a function of the position y on the bisector. What is the asymptotic behaviour for ygg d? abclist
Solution:
abclist abc The partial field vectors vecE_+ and vecE_- are displayed in the figure. center includegraphicswidth.mm#image_path:dipolfield-along-x# center The net field strength E is given by E E_- - E_+ k_C qleftfracx-d/^-fracx+d/^right k_C q fracx+d/^-x-d/^leftx^-d/^right^ k_C q fracx^+x d/+d/^-x^+x d/-d/^leftx^-d/^right^ k_C fracq x dleftx^-d/^right^ For xgg d all mands but the leading term x^ are negligible in the denominator. The field strength is approximately equal to E &approx k_C fracq x dx^ k_C fracq dx^ abc The figure shows how the net electric field vector E deps on the partial field vectors E_+ and E_-. center includegraphicswidthmm#image_path:dipolfield-along-y# center Using similar triangles it follows fracEE_+ fracdr rightarrow E E_+fracdr k_C fracqr^fracdrk_C fracq dr^ k_C fracq dleftd/^+y^right^/ For ygg d the term in d can be neglected in the denominator. The field strength is approximately equal to E &approx k_Cfracq dy^^/ k_Cfracq dy^ abclist It turns out that the field strength of a dipole decreases like /r^ for rgg d. This is different from the behaviour of a single po charge where the field drops off like /r^ inverse square law.
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Electric Field by by
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