E E 325 - HW 1 (Chp. 2)

# E E 325 - HW 1 (Chp. 2) - z positive let ρ υ = 40 xyz C/m...

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Homework #1, Chapter 2 1. A charge Q 0 = 1 nC is located in free space at P ( a ,0,0). Prepare a sketch of the magnitude of the force on Q 0 , as a function of a , 0 a 5m, produced by two other charges, Q 1 = 1 C at (0,1,0) and Q 2 =: (a) 1 C at (0,-1,0); (b) - 1 C at (0,-1,0). 2. A point charge Q 1 = 10 µ C, is located at P 1 (1,2,3) in free space, while Q 2 = -5 µ C is at P 2 (1,2,10). (a) Find the vector force exerted on Q 2 by Q 1 . (b) Find the coordinates of P 3 at which a point charge Q 3 experiences no force. 3. In free space, let Q 1 = 10 nC be at P 1 (0,-4,0), and Q 2 = 20 nC be at P 2 (0,0,4). (a) Find E at the origin. (b) Where should a 30-nC point charge be located so that E = 0 at the origin? 4. A 5-nC point charge is located at A (2,-1,-3) in free space. (a) Find E at the origin. (b) Plot | E ( x ,0,0)| vs. x , -10 x 10 m. (c) What is | E ( x ,0,0)| max ? 5. For x, y , and
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Unformatted text preview: z positive, let ρ υ = 40 xyz C/m 3 . Find the total charge within the region defined by: (a) 0 ≤ x,y,z ≤ 2; (b) x = 0, y = 0, 0 ≤ 2 x + 3 y ≤ 10, 0 ≤ z ≤ 2. 6. Volume charge density within the operating region of a parallel-plate vacuum diode is given by = − ( 4 9 ) ∈ V d − 4 3 x − 2 3 , where the cathode is located at x = 0 and the anode at x = d . The voltage between anode and cathode is V . If the total charge in a 1-m 2 cross section is -20 nC and: (a) d = 8 mm, find V ; (b) V = 24 V, find d . (c) If d = 8 mm and V = 24 V, sketch vs. x . 7. That portion of the z axis for which -2 < z < 2 m carries a nonuniform charge density of z 2 + 1 nC/m in free space. There are no other charges anywhere. Find E at: (a) P A (1,0,0); (b) P B (2,0,0)....
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