scalar and vector fields - wordpress.com · 2/1/2015 · scalar and vector fields •a scalar...
TRANSCRIPT
![Page 1: Scalar and Vector Fields - WordPress.com · 2/1/2015 · Scalar and Vector Fields •A scalar field is a function that gives us a single value of some variable for every point in](https://reader036.vdocument.in/reader036/viewer/2022062317/5fc2a4342df656188f677376/html5/thumbnails/1.jpg)
![Page 2: Scalar and Vector Fields - WordPress.com · 2/1/2015 · Scalar and Vector Fields •A scalar field is a function that gives us a single value of some variable for every point in](https://reader036.vdocument.in/reader036/viewer/2022062317/5fc2a4342df656188f677376/html5/thumbnails/2.jpg)
Scalar and Vector Fields
• A scalar field is a function that gives us a single value of some variable for every point in space.
• Examples: voltage, current, energy, temperature
• A vector is a quantity which has both a magnitude and a direction in space.
• Examples: velocity, momentum, acceleration and force
![Page 3: Scalar and Vector Fields - WordPress.com · 2/1/2015 · Scalar and Vector Fields •A scalar field is a function that gives us a single value of some variable for every point in](https://reader036.vdocument.in/reader036/viewer/2022062317/5fc2a4342df656188f677376/html5/thumbnails/3.jpg)
Example of a Scalar Field
![Page 4: Scalar and Vector Fields - WordPress.com · 2/1/2015 · Scalar and Vector Fields •A scalar field is a function that gives us a single value of some variable for every point in](https://reader036.vdocument.in/reader036/viewer/2022062317/5fc2a4342df656188f677376/html5/thumbnails/4.jpg)
4
Vector FieldsVector (magnitude, direction) at every point in
space
Example: Velocity vector field - jet stream
![Page 5: Scalar and Vector Fields - WordPress.com · 2/1/2015 · Scalar and Vector Fields •A scalar field is a function that gives us a single value of some variable for every point in](https://reader036.vdocument.in/reader036/viewer/2022062317/5fc2a4342df656188f677376/html5/thumbnails/5.jpg)
Vector Fields Explained
![Page 6: Scalar and Vector Fields - WordPress.com · 2/1/2015 · Scalar and Vector Fields •A scalar field is a function that gives us a single value of some variable for every point in](https://reader036.vdocument.in/reader036/viewer/2022062317/5fc2a4342df656188f677376/html5/thumbnails/6.jpg)
Examples of Vector Fields
![Page 7: Scalar and Vector Fields - WordPress.com · 2/1/2015 · Scalar and Vector Fields •A scalar field is a function that gives us a single value of some variable for every point in](https://reader036.vdocument.in/reader036/viewer/2022062317/5fc2a4342df656188f677376/html5/thumbnails/7.jpg)
Examples of Vector Fields
![Page 8: Scalar and Vector Fields - WordPress.com · 2/1/2015 · Scalar and Vector Fields •A scalar field is a function that gives us a single value of some variable for every point in](https://reader036.vdocument.in/reader036/viewer/2022062317/5fc2a4342df656188f677376/html5/thumbnails/8.jpg)
Examples of Vector Fields
![Page 9: Scalar and Vector Fields - WordPress.com · 2/1/2015 · Scalar and Vector Fields •A scalar field is a function that gives us a single value of some variable for every point in](https://reader036.vdocument.in/reader036/viewer/2022062317/5fc2a4342df656188f677376/html5/thumbnails/9.jpg)
VECTOR REPRESENTATION
3 PRIMARY COORDINATE SYSTEMS:
• RECTANGULAR
• CYLINDRICAL
• SPHERICAL
Choice is based on symmetry of problem
Examples:
Sheets - RECTANGULAR
Wires/Cables - CYLINDRICAL
Spheres - SPHERICAL
![Page 10: Scalar and Vector Fields - WordPress.com · 2/1/2015 · Scalar and Vector Fields •A scalar field is a function that gives us a single value of some variable for every point in](https://reader036.vdocument.in/reader036/viewer/2022062317/5fc2a4342df656188f677376/html5/thumbnails/10.jpg)
![Page 11: Scalar and Vector Fields - WordPress.com · 2/1/2015 · Scalar and Vector Fields •A scalar field is a function that gives us a single value of some variable for every point in](https://reader036.vdocument.in/reader036/viewer/2022062317/5fc2a4342df656188f677376/html5/thumbnails/11.jpg)
![Page 12: Scalar and Vector Fields - WordPress.com · 2/1/2015 · Scalar and Vector Fields •A scalar field is a function that gives us a single value of some variable for every point in](https://reader036.vdocument.in/reader036/viewer/2022062317/5fc2a4342df656188f677376/html5/thumbnails/12.jpg)
![Page 13: Scalar and Vector Fields - WordPress.com · 2/1/2015 · Scalar and Vector Fields •A scalar field is a function that gives us a single value of some variable for every point in](https://reader036.vdocument.in/reader036/viewer/2022062317/5fc2a4342df656188f677376/html5/thumbnails/13.jpg)
![Page 14: Scalar and Vector Fields - WordPress.com · 2/1/2015 · Scalar and Vector Fields •A scalar field is a function that gives us a single value of some variable for every point in](https://reader036.vdocument.in/reader036/viewer/2022062317/5fc2a4342df656188f677376/html5/thumbnails/14.jpg)
![Page 15: Scalar and Vector Fields - WordPress.com · 2/1/2015 · Scalar and Vector Fields •A scalar field is a function that gives us a single value of some variable for every point in](https://reader036.vdocument.in/reader036/viewer/2022062317/5fc2a4342df656188f677376/html5/thumbnails/15.jpg)
![Page 16: Scalar and Vector Fields - WordPress.com · 2/1/2015 · Scalar and Vector Fields •A scalar field is a function that gives us a single value of some variable for every point in](https://reader036.vdocument.in/reader036/viewer/2022062317/5fc2a4342df656188f677376/html5/thumbnails/16.jpg)
![Page 17: Scalar and Vector Fields - WordPress.com · 2/1/2015 · Scalar and Vector Fields •A scalar field is a function that gives us a single value of some variable for every point in](https://reader036.vdocument.in/reader036/viewer/2022062317/5fc2a4342df656188f677376/html5/thumbnails/17.jpg)
![Page 18: Scalar and Vector Fields - WordPress.com · 2/1/2015 · Scalar and Vector Fields •A scalar field is a function that gives us a single value of some variable for every point in](https://reader036.vdocument.in/reader036/viewer/2022062317/5fc2a4342df656188f677376/html5/thumbnails/18.jpg)
![Page 19: Scalar and Vector Fields - WordPress.com · 2/1/2015 · Scalar and Vector Fields •A scalar field is a function that gives us a single value of some variable for every point in](https://reader036.vdocument.in/reader036/viewer/2022062317/5fc2a4342df656188f677376/html5/thumbnails/19.jpg)
![Page 20: Scalar and Vector Fields - WordPress.com · 2/1/2015 · Scalar and Vector Fields •A scalar field is a function that gives us a single value of some variable for every point in](https://reader036.vdocument.in/reader036/viewer/2022062317/5fc2a4342df656188f677376/html5/thumbnails/20.jpg)
![Page 21: Scalar and Vector Fields - WordPress.com · 2/1/2015 · Scalar and Vector Fields •A scalar field is a function that gives us a single value of some variable for every point in](https://reader036.vdocument.in/reader036/viewer/2022062317/5fc2a4342df656188f677376/html5/thumbnails/21.jpg)
![Page 22: Scalar and Vector Fields - WordPress.com · 2/1/2015 · Scalar and Vector Fields •A scalar field is a function that gives us a single value of some variable for every point in](https://reader036.vdocument.in/reader036/viewer/2022062317/5fc2a4342df656188f677376/html5/thumbnails/22.jpg)
![Page 23: Scalar and Vector Fields - WordPress.com · 2/1/2015 · Scalar and Vector Fields •A scalar field is a function that gives us a single value of some variable for every point in](https://reader036.vdocument.in/reader036/viewer/2022062317/5fc2a4342df656188f677376/html5/thumbnails/23.jpg)
![Page 24: Scalar and Vector Fields - WordPress.com · 2/1/2015 · Scalar and Vector Fields •A scalar field is a function that gives us a single value of some variable for every point in](https://reader036.vdocument.in/reader036/viewer/2022062317/5fc2a4342df656188f677376/html5/thumbnails/24.jpg)
![Page 25: Scalar and Vector Fields - WordPress.com · 2/1/2015 · Scalar and Vector Fields •A scalar field is a function that gives us a single value of some variable for every point in](https://reader036.vdocument.in/reader036/viewer/2022062317/5fc2a4342df656188f677376/html5/thumbnails/25.jpg)
![Page 26: Scalar and Vector Fields - WordPress.com · 2/1/2015 · Scalar and Vector Fields •A scalar field is a function that gives us a single value of some variable for every point in](https://reader036.vdocument.in/reader036/viewer/2022062317/5fc2a4342df656188f677376/html5/thumbnails/26.jpg)
![Page 27: Scalar and Vector Fields - WordPress.com · 2/1/2015 · Scalar and Vector Fields •A scalar field is a function that gives us a single value of some variable for every point in](https://reader036.vdocument.in/reader036/viewer/2022062317/5fc2a4342df656188f677376/html5/thumbnails/27.jpg)
![Page 28: Scalar and Vector Fields - WordPress.com · 2/1/2015 · Scalar and Vector Fields •A scalar field is a function that gives us a single value of some variable for every point in](https://reader036.vdocument.in/reader036/viewer/2022062317/5fc2a4342df656188f677376/html5/thumbnails/28.jpg)
![Page 29: Scalar and Vector Fields - WordPress.com · 2/1/2015 · Scalar and Vector Fields •A scalar field is a function that gives us a single value of some variable for every point in](https://reader036.vdocument.in/reader036/viewer/2022062317/5fc2a4342df656188f677376/html5/thumbnails/29.jpg)
![Page 30: Scalar and Vector Fields - WordPress.com · 2/1/2015 · Scalar and Vector Fields •A scalar field is a function that gives us a single value of some variable for every point in](https://reader036.vdocument.in/reader036/viewer/2022062317/5fc2a4342df656188f677376/html5/thumbnails/30.jpg)
![Page 31: Scalar and Vector Fields - WordPress.com · 2/1/2015 · Scalar and Vector Fields •A scalar field is a function that gives us a single value of some variable for every point in](https://reader036.vdocument.in/reader036/viewer/2022062317/5fc2a4342df656188f677376/html5/thumbnails/31.jpg)
![Page 32: Scalar and Vector Fields - WordPress.com · 2/1/2015 · Scalar and Vector Fields •A scalar field is a function that gives us a single value of some variable for every point in](https://reader036.vdocument.in/reader036/viewer/2022062317/5fc2a4342df656188f677376/html5/thumbnails/32.jpg)
![Page 33: Scalar and Vector Fields - WordPress.com · 2/1/2015 · Scalar and Vector Fields •A scalar field is a function that gives us a single value of some variable for every point in](https://reader036.vdocument.in/reader036/viewer/2022062317/5fc2a4342df656188f677376/html5/thumbnails/33.jpg)
![Page 34: Scalar and Vector Fields - WordPress.com · 2/1/2015 · Scalar and Vector Fields •A scalar field is a function that gives us a single value of some variable for every point in](https://reader036.vdocument.in/reader036/viewer/2022062317/5fc2a4342df656188f677376/html5/thumbnails/34.jpg)
![Page 35: Scalar and Vector Fields - WordPress.com · 2/1/2015 · Scalar and Vector Fields •A scalar field is a function that gives us a single value of some variable for every point in](https://reader036.vdocument.in/reader036/viewer/2022062317/5fc2a4342df656188f677376/html5/thumbnails/35.jpg)
![Page 36: Scalar and Vector Fields - WordPress.com · 2/1/2015 · Scalar and Vector Fields •A scalar field is a function that gives us a single value of some variable for every point in](https://reader036.vdocument.in/reader036/viewer/2022062317/5fc2a4342df656188f677376/html5/thumbnails/36.jpg)
![Page 37: Scalar and Vector Fields - WordPress.com · 2/1/2015 · Scalar and Vector Fields •A scalar field is a function that gives us a single value of some variable for every point in](https://reader036.vdocument.in/reader036/viewer/2022062317/5fc2a4342df656188f677376/html5/thumbnails/37.jpg)
![Page 38: Scalar and Vector Fields - WordPress.com · 2/1/2015 · Scalar and Vector Fields •A scalar field is a function that gives us a single value of some variable for every point in](https://reader036.vdocument.in/reader036/viewer/2022062317/5fc2a4342df656188f677376/html5/thumbnails/38.jpg)
![Page 39: Scalar and Vector Fields - WordPress.com · 2/1/2015 · Scalar and Vector Fields •A scalar field is a function that gives us a single value of some variable for every point in](https://reader036.vdocument.in/reader036/viewer/2022062317/5fc2a4342df656188f677376/html5/thumbnails/39.jpg)
![Page 40: Scalar and Vector Fields - WordPress.com · 2/1/2015 · Scalar and Vector Fields •A scalar field is a function that gives us a single value of some variable for every point in](https://reader036.vdocument.in/reader036/viewer/2022062317/5fc2a4342df656188f677376/html5/thumbnails/40.jpg)
![Page 41: Scalar and Vector Fields - WordPress.com · 2/1/2015 · Scalar and Vector Fields •A scalar field is a function that gives us a single value of some variable for every point in](https://reader036.vdocument.in/reader036/viewer/2022062317/5fc2a4342df656188f677376/html5/thumbnails/41.jpg)
![Page 42: Scalar and Vector Fields - WordPress.com · 2/1/2015 · Scalar and Vector Fields •A scalar field is a function that gives us a single value of some variable for every point in](https://reader036.vdocument.in/reader036/viewer/2022062317/5fc2a4342df656188f677376/html5/thumbnails/42.jpg)
![Page 43: Scalar and Vector Fields - WordPress.com · 2/1/2015 · Scalar and Vector Fields •A scalar field is a function that gives us a single value of some variable for every point in](https://reader036.vdocument.in/reader036/viewer/2022062317/5fc2a4342df656188f677376/html5/thumbnails/43.jpg)
![Page 44: Scalar and Vector Fields - WordPress.com · 2/1/2015 · Scalar and Vector Fields •A scalar field is a function that gives us a single value of some variable for every point in](https://reader036.vdocument.in/reader036/viewer/2022062317/5fc2a4342df656188f677376/html5/thumbnails/44.jpg)
![Page 45: Scalar and Vector Fields - WordPress.com · 2/1/2015 · Scalar and Vector Fields •A scalar field is a function that gives us a single value of some variable for every point in](https://reader036.vdocument.in/reader036/viewer/2022062317/5fc2a4342df656188f677376/html5/thumbnails/45.jpg)
![Page 46: Scalar and Vector Fields - WordPress.com · 2/1/2015 · Scalar and Vector Fields •A scalar field is a function that gives us a single value of some variable for every point in](https://reader036.vdocument.in/reader036/viewer/2022062317/5fc2a4342df656188f677376/html5/thumbnails/46.jpg)
SEE YOU NEXT WEEK
Optional Homework:
Solve at least 3 vector problems byyourself.