Spring2023_ECE3110_Homework#9_Solutions

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University of Colorado, Colorado Springs *

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3110

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Mechanical Engineering

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Oct 30, 2023

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1/8 ECE3110 (Spring 2023) Homework #9 Solutions April 13, 2023 1. A ring placed along ? 2 + ? 2 = 4, ? = 0 carries a uniform charge of 5 𝜇?/𝑚. (a) Find ? at P (3, 0, 0). (b) If two identical point charges 𝑄 are placed at (0, -3, 0) and (0, 3, 0) in addition to the ring, find the value of 𝑄 such that ? = 0 at P. Solution:
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3/8 2. A grounded metal sheet is located in the ? = 0 plane, while a point charge 𝑄 is located at (0, 0, 𝑎) . Find the force acting on a point charge – 𝑄 placed at ( 𝑎, 0, 𝑎). Solution:
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5/8 3. Four charges are arranged as shown in Figure 2. (a) Find the electric field intensity at any point in space. (b) Show that the electric field intensity is perpendicular to the two dotted lines shown (at 45°). Figure 2 Solution:
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7/8 4. Electric charge is distributed along an arc located in the xy-plane and defined by 𝑟 = 2 𝑐𝑚 and 0 ≤ 𝜙 ≤ ? 4 ⁄ . If ? 𝑙 = 5 (µ? 𝑚 ), find ? at (0, 0, z) and then evaluate it at (a) the origin, (b) z = 5 cm, and (c) z = -5 cm.
8/8 5. A line of charge with uniform density ? 𝑙 = 8 (µ? 𝑚 ) exists in air along the z-axis between z=0 and z=5 cm. Find ? at (0, 10 cm, 0).

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