Workshop01VectorCalc

Workshop01VectorCalc - ECE 3030 Electromagnetic Fields and...

Info icon This preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
ECE 3030: Electromagnetic Fields and Waves Fall 2009 WORKSHOP 1 INSTRUCTOR NOTES: Vector Calculus Reminder: Help students as they need it. Date: Tuesday 9/3 1. Problem 2.9: Let ~ B = 2ˆ x + 3ˆ z . (f) The magnitude of | B | = 2 2 + 3 2 = 13. (i) The unit vector= ~ B | ~ B | = 1 13 (2ˆx + 3ˆ z). 2. Problem 2.17 A vector ~ F is given by ~ F = 3 r sin φ ˆ r + r 3 cos φ ˆ φ . a. Evaluate H ~ F · d around the contour ABCDA shown in Figure 1, where a = 1 m and b = 2 m. b. Find the expression for ~ ∇ × ~ F. c. Evaluate R ( ~ ∇ × ~ F) · ~ d a over the sur- face enclosed by the ABCDA contour. Be careful with the direction of ~ d a . Check your answers to (a) and (c) with Stokes’ Theorem. y x a b A B C D Figure 1: Contour ABCDA sur- rounds the shaded area. Solution: Matching results from a contour integral to a surface integral demonstrates Stokes Theorem. In general, ~ d = ˆxd x + ˆyd y + ˆ zd z , and in cylindrical coordinates, this becomes ~ d = ˆ rd r + ˆ φr d r . a. Path D A: r = 1, ~ d = d φ ˆ φ = 1d φ ˆ φ with d r = 0.
Image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern