ECE309-2009-hw2

# ECE309-2009-hw2 - ~ E = 1 r 2(1-cos 3 r ˆ r V m(b A charge...

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

ECE 3209 — Electromagnetic Fields University of Virginia Fall 2009 Homework # 2 — Vector Calculus and Electric Fields Due: Friday, September 11 1. Verify Gauss’s Theorem for the function, ~ F = r 2 sin θ ˆ r + 4 r 2 cos θ ˆ θ + r 2 tan θ ˆ φ using the volume of the “ice cream cone” shown below. The top surface is spherical with radius R and centered at the origin. 2. Cheng, P. 2-32 . 3. Cheng, P. 2-36 . 4. Using the fundamental theorems of vector calculus, show that (a) Z volume ( ~ t ) dv = Z surface t d~a (b) Z volume ( t ~ 2 u - u ~ 2 t ) dv = Z surface ( t ~ u - u ~ t ) · d~a

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

View Full Document
This last relation is known as Green’s Theorem
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ~ E = 1 r 2 (1-cos 3 r ) ˆ r V / m (b) A charge distribution, ρ = exp(-r ) μ C / m 3 , is set up in empty space. Find the electric ﬁeld associated with this charge. 6. Find the electric ﬁeld a distance z above one end of a straight line segment of length L that carries a uniform linear charge density of λ . Check that your formula is consistent with the case z ± L . 7. Cheng, P. 3-8 . 8. Cheng, P. 3-9 ....
View Full Document

{[ snackBarMessage ]}

### What students are saying

• 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.

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

• 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.

Dana University of Pennsylvania ‘17, Course Hero Intern

• 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.

Jill Tulane University ‘16, Course Hero Intern