P22_044

# P22_044 - x if q 3 &amp;amp;gt; 0 and points towards + x if...

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44. We are looking for a charge q which, when placed at the origin, experiences ~ F net =0,where ~ F net = ~ F 1 + ~ F 2 + ~ F 3 . The magnitude of these individual forces are given by Coulomb’s law, Eq. 22-1, and without loss of generality we assume q> 0. The charges q 1 (+6 µ C), q 2 ( 4 µ C), and q 3 (unknown), are located on the + x axis, so that we know ~ F 1 points towards x , ~ F 2 points towards + x ,and ~ F 3 points towards
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Unformatted text preview: x if q 3 &gt; 0 and points towards + x if q 3 &lt; 0. Therefore, with r 1 = 8 m, r 2 = 16 m and r 3 = 24 m, we have 0 = k q 1 q r 2 1 + k | q 2 | q r 2 2 k q 3 q r 2 3 . Simplifying, this becomes 0 = 6 8 2 + 4 16 2 q 3 24 2 where q 3 is now understood to be in C. Thus, we obtain q 3 = 45 C....
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