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Unformatted text preview: CHAPTER 2 2.1. Four 10nC positive charges are located in the z = 0 plane at the corners of a square 8cm on a side. A fifth 10nC positive charge is located at a point 8cm distant from the other charges. Calculate the magnitude of the total force on this fifth charge for ² = ² : Arrange the charges in the xy plane at locations (4,4), (4,4), (4,4), and (4,4). Then the fifth charge will be on the z axis at location z = 4 √ 2, which puts it at 8cm distance from the other four. By symmetry, the force on the fifth charge will be zdirected, and will be four times the z component of force produced by each of the four other charges. F = 4 √ 2 × q 2 4 π² d 2 = 4 √ 2 × (10 − 8 ) 2 4 π (8 . 85 × 10 − 12 )(0 . 08) 2 = 4 . × 10 − 4 N 2.2. Two point charges of Q 1 coulombs each are located at (0,0,1) and (0,0,1). (a) Determine the locus of the possible positions of a third charge Q 2 where Q 2 may be any positive or negative value, such that the total field E = 0 at (0,1,0): The total field at (0,1,0) from the two Q 1 charges (where both are positive) will be E 1 (0 , 1 , 0) = 2 Q 1 4 π² R 2 cos45 ◦ a y = Q 1 4 √ 2 π² a y where R = √ 2. To cancel this field, Q 2 must be placed on the y axis at positions y > 1 if Q 2 > 0, and at positions y < 1 if Q 2 < 0. In either case the field from Q 2 will be E 2 (0 , 1 , 0) = − Q 2  4 π² a y and the total field is then E t = E 1 + E 2 = · Q 1 4 √ 2 π² −  Q 2  4 π² ¸ = 0 Therefore Q 1 √ 2 =  Q 2  ( y − 1) 2 ⇒ y = 1 ± 2 1 / 4 s  Q 2  Q 1 where the plus sign is used if Q 2 > 0, and the minus sign is used if Q 2 < 0. (b) What is the locus if the two original charges are Q 1 and − Q 1 ? In this case the total field at (0,1,0) is E 1 (0 , 1 , 0) = − Q 1 / (4 √ 2 π² ) a z , where the positive Q 1 is located at the positive z (= 1) value. We now need Q 2 to lie along the line x = 0, y = 1 in order to cancel the field from the positive and negative Q 1 charges. Assuming Q 2 is located at (0 , 1 , z ), the total field is now E t = E 1 + E 2 = − Q 1 4 √ 2 π² a z +  Q 2  4 π² z 2 = 0 or z = ± 2 1 / 4 p  Q 2  /Q 1 , where the plus sign is used if Q 2 < 0, and the minus sign if Q 2 > 0. 1 2.3. Point charges of 50nC each are located at A (1 , , 0), B ( − 1 , , 0), C (0 , 1 , 0), and D (0 , − 1 , 0) in free space. Find the total force on the charge at A ....
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This homework help was uploaded on 04/01/2008 for the course EE 1 taught by Professor Joshi during the Fall '08 term at UCLA.
 Fall '08
 Joshi
 Electrical Engineering

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