1. Document that explains the chosen concept to the animator 1

2. Vector fields in 2D Authors Anura.B.Kenkre Course Name: Mathematical Physics 2

3. Learning Objectives After interacting with this Learning Object, the learner will be able to: Determine the vector field components given the co-ordinates of a point in space. Determine the vector field given the individual components. Determine the magnitude of vector function. Determine the direction of vector function. Predict how the vector field will look in 2D. 3

4. Definitions of the components/Keywords: 5 3 2 4 1 4 Vector field is the one where the physical property associated with every point is expressed as vector quantity. At every point this vector function is specified by vector with certain magnitude and direction - called vector point.

5. Master layout or diagram Make a schematic diagram of the concept Explain to the animator about the beginning and ending of the process. Draw image big enough for explaining. In above image, identify and label different components of the process/phenomenon. (These are like characters in a film)‏ Illustrate the basic flow of action by using arrows. Use BOLD lines in the diagram, (minimum 2pts.)‏ In the slide after that, provide the definitions of ALL the labels used in the diagram 5 3 2 4 1 INSTRUCTIONS SLIDE 5

6. Master layout or diagram You may have multiple master layouts. –In this case, number the master layout. ( e.g. Master layout 1)‏ – Each Master layout should be followed by the stepwise description of the animation stages related to it. 5 3 2 4 1 INSTRUCTIONS SLIDE 6

7. 7 IMPORTANT NOTE TO THE ANIMATOR: All the instructions/labels or anything WRITTEN in blue are CONTENT NOT TO BE DISPLAYED! All the instructions WRITTEN in black are CONTENT TO BE DISPLAYED! This is not applicable for images as there can be overlapping of these colours there. This should be followed for all the instructions, labels,etc… Kindly keep a note of this while displaying text in the animation.

8. VECTOR FIELDS Measure length Magnitude: Direction: Measure direction x y (1,1) At point: 11 VECTOR FIELD IN 2D (1,1) Show entire field Master Layout 5 3 2 4 1 8 This entire area will be coded so that every point there will have different co-ordinates The plotted vector field will be plotted here The equation for the vector field will be displayed here Calculations will be displayed here Co-ordinates and the corresponding components will be displayed here Interactivity options

9. Animation design Please see the design template provided in the next slide. This is a sample template, and you are free to change as per your design requirements. Try and recreate the sections/subsections as shown in the template. 1 5 2 4 3 9

10. Lets Learn! Credits Definitions Test your understanding (questionnaire) ‏ Lets Sum up (summary) ‏ Want to know more… (Further Reading) ‏ Slide 3 Slide 4 Slide 24-26 Slide 29 Slide 27 Use STAM template 10 VECTOR FIELDS Measure length Magnitude: Direction: Measure direction x y (1,1) At point: 11 VECTOR FIELD IN 2D (1,1) Show entire field

11. Explain the process 1 5 3 2 4 In this step, use an example to explain the concept. It can be an analogy, a scenario, or an action which explains this concept/process/topic Try to use examples from day-to-day life to make it more clear You have to describe what steps the animator should take to make your concept come alive as a series of moving images. Keep the examples simple to understand, and also to illustrate/animate. 11

12. Stepwise description of process The goal of the document is to provide instructions to an animator who is not a expert. You have to describe what steps the animator should take to make your concept come alive as a moving visualization. Use one slide per step. This will ensure clarity of the explanation. Add a image of the step in the box, and the details in the table below the box. You can use any images for reference, but mention about it's copyright status The animator will have to re-draw / re-create the drawings Add more slides as per the requirement of the animation 1 5 3 2 4 12

13. Step 1: 1 5 3 2 4 Description of the action/ interactivity Refer to slide 14 The opening screen will look like slide 14. 13

14. 14 VECTOR FIELDS At point: Vector components are: V x V y SELECT Show entire field VECTOR FIELD IN 2D

15. Step 2: 1 5 3 2 4 Description of the action/ interactivity Refer to slide 19 Initially ask the user to select a vector function. When the user clicks on the drop down menu for vector functions, display the options given on slide 16. Here the button for ‘show entire field’ should be disabled. When the user selects an option go to slide 17. 15

16. 16 Vector functions list

17. Step 2: 1 5 3 2 4 Description of the action/ interactivity Refer to slide 19 When the user selects a function, allow him to click at any one point in the area marked as vector function in 2D For plotting the vector function in 2D : This area will have points that are previously coded by you each having a specific co –ordinate along the axes…when the user clicks on any point, the co-ordinates of that point will be displayed under the box ‘at point’. For the selected vector function, the x co-ordinate will be displayed at Vx. For the selected vector function, the y co-ordinate will be displayed at Vy. An arrow should be displayed at the point selected by the user. The length of the arrow will be given by The direction in which the arrow should point will be given by Here θ denotes the angle made by the vector with the x axis. (this axis should be drawn from that point parallel to the actual X-axis). In the tanθ formula, ‘y’ is the co-ordinate of the j unit vector and ‘x’ is the co-ordinate of the i unit vector. Any angle measured in the anti-clockwise direction is considered positive and vice versa. As the user selects different points,show the current point in red and the previous points in black. Now,as soon as the user selects the vector function from the drop down menu, That function will be displayed under vector function on the right hand side of the screen.. Below this the calculations for the length and the direction should appear. Here the button for ‘show entire field’ should be enabled. If the user clicks on ‘show entire field’ then you should yourself put different values in the function for x,y,z and generate the field in all space(like arrows shown in blue). Display this under vector function in 2D. The above steps are explained taking an example on slide 19. 17

18. Step 3: 1 5 3 2 4 Description of the action/ interactivity Refer to slide 19 Shown on the right hand side are two symbols. First symbol is that of a protractor. Allow the user to drag it into the workspace and try and measure the angle that the vector makes with the x axis. Give a mouse over for protractor saying “Drag this to measure the angle made by the vector with the x axis” and for ruler saying “Drag this to measure the length of the vector” Make sure that this angle matches with the calculated value. Next symbol is that of a ruler. Allow the user to drag it into the workspace and measure the length of the vector arrow. Calibrate the ruler accordingly. Make sure that the length of the arrow matches with the calculated length. Highlight the selected point(in space)under the vector function in 2D. Important instructions to the animator: While plotting the vector field for cos and sine functions, see to it that you cover numbers up to 360 on the x axis… So you can space the intervals accordingly…on the x axis.. 18

19. 19 VECTOR FIELDS Measure length Magnitude: Direction: Measure direction x y (1,1) At point: Vector components are: V x V y 11 VECTOR FIELD IN 2D (1,1) Show entire field

20. Interactivity and Boundary limits In this section, you will add the ‘Interactivity’ options to the animation. Use the template in the next slide to give the details. Insert the image of the step/s (explained earlier in the Section 3) in the box, and provide the details in the table below. The details of Interactivity could be: Types: Drop down, Slider bar, Data inputs etc. Options: Select one, Multiple selections etc Boundary Limits: Values of the parameters, which won’t show results after a particular point Results: Explain the effect of the interaction in this column Add more slides if necessary 1 2 5 3 4 20

21. 1 5 3 2 4 Slides 13-19 Instructions for the animator Instruction to the learner Results and Output Boundary limits Interactivity type (IO1/IO2..) ‏ Interactivity option 1: Step No: 21

22. INSTRUCTIONS SLIDE Self- Assessment Questionnaire for Learners Please provide a set of questions that a user can answer based on the LO. They can be of the following types: –These questions should be 5 in number and can be of objective type (like MCQ, Match the columns, Yes or No, Sequencing, Odd One Out). –The questions can also be open-ended. The user would be asked to think about the question. The author is requested to provide hints if possible, but a full answer is not necessary. –One can include questions, for which the user will need to interact with the LO (with certain parameters) in order to answer it. 22

23. INSTRUCTIONS SLIDE Please make sure that the questions can be answered by interacting with the LO. It is better to avoid questions based purely on recall. Questionnaire for users to test their understanding 23

24. 1)Given the field below, can you predict the equation which would best describe this field?? I II 1. 4 Answers: A) B) C) Questionnaire Answers:1)B Feedback: If user clicks correct answer then display “Correct! Make sure you can explain the reasoning!” If user clicks incorrect answer then display “Observe the vector functions carefully, play with the simulation and Try again!” II x y

25. 2)Given the field below, can you predict the equation which would best describe this field?? I II 1. 4 Answers: A) B) C) D) Questionnaire Answers:2)D Feedback: If user clicks correct answer then display “Correct! Make sure you can explain the reasoning!” If user clicks incorrect answer then display “Observe the vector functions carefully, play with the simulation and Try again!” II x y

26. 3)Given the field below, can you predict the equation which would best describe this field?? I II 1. 4 Questionnaire Correct answer:3)C Feedback: If user clicks correct answer then display “Correct! Make sure you can explain the reasoning!” If user clicks incorrect answer then display “Try to plot the vector function by substituting different values of x and Try again!” II x y Answers:

27. Links for further reading Books: Introduction to Electrodynamics (chapter 1) -David J. Griffiths 27

28. INSTRUCTIONS SLIDE Please provide points to remember to understand the concept/ key terms of the animation The summary will help the user in the quick review of the concept. Summary 28

29. Summary At every point in space, a vector function is specified by vector with certain magnitude and direction - called vector point. The magnitude of the vector function(V) is calculated using the formula: The direction of the vector function at a particular point in space is given by: 29