ECE309-2009-hw2

ECE309-2009-hw2 - ~ E = 1 r 2 (1-cos 3 r ) r V / m (b) A...

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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 td~a (b) Z volume ( t ~ 2 u - u ~ 2 t ) dv = Z surface ( t ~ u - u ~ t ) · d~a
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This last relation is known as Green’s Theorem . 5. (a) Find the charge distribution that generates an electrostatic field of the form,
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Unformatted text preview: ~ E = 1 r 2 (1-cos 3 r ) r V / m (b) A charge distribution, = exp(-r ) C / m 3 , is set up in empty space. Find the electric eld associated with this charge. 6. Find the electric eld a distance z above one end of a straight line segment of length L that carries a uniform linear charge density of . Check that your formula is consistent with the case z L . 7. Cheng, P. 3-8 . 8. Cheng, P. 3-9 ....
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ECE309-2009-hw2 - ~ E = 1 r 2 (1-cos 3 r ) r V / m (b) A...

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