- #1
Jefferson
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Homework Statement
There is a −3 µC point charge at (0,0,4) and a +3 µC point charge at (0,0,-4). What is the magnitude and direction of the electric field at point (0,0,8)? What is the magnitude and direction of the electric field at point (0,0,8)? [/B]
Homework Equations
[itex][/itex][itex]E = \frac{ k_e q }{ r^2 }<b>[<b>/itex]</b></b>[/B]<br /> <br /> <h2>The Attempt at a Solution</h2> <br /> It should be as simple as just adding the electric field caused by each point charge.<br /> <b>[itex][/itex]</b>[itex](0,0,8)[<b>/itex]</b>:<br /> <b>[itex][/itex]</b>[itex](0,0,8) - (0,0,4) = (0,0,4)[/itex]<b><br /> [itex][/itex]</b>[itex](0,0,8) - (0,0,-4) = (0,0,12)[/itex]<b><br /> <b>[itex][/itex]</b>[itex]\frac{ k_e[/itex]</b>[itex]<b>−3 \mu C (0,0,4) }{ 4^3} + <b>\frac{ <b>k_e</b> <b>3 \mu C (0,0,12) }{ 12^3 }</b></b></b>[/itex]<b><b><b><br /> <br /> -1685.625 + 187.29166 = -1498.33334<br /> However, the answer I should be getting (apparently) is 609<br /> <br /> (4,4,0):<br /> <b><b>(4,4,0) </b>- (0,0,4) = (4,4,-4)<br /> <b>(4,4,0)</b> - (0,0,-4) = (4,4,4)<br /> <br /> <b>k<sub>e</sub> <b>−3 µC (4,4,-4) / (4^2 + 4^2 + 4^2)^(3/2) + <b>k<sub>e</sub> <b>3 µC <b>(4,4,4) / (4^2 + 4^2 + 4^2)^(3/2)<br /> <br /> <b>k<sub>e</sub> <b>−3 µC (4,4,-4) / (48)^(3/2) + <b>k<sub>e</sub> <b>3 µC <b>(4,4,4) / (48)^(3/2)<br /> <br /> (-324.4, -<b>324.4, <b>324.4) + (<b>324.4,<b>324.4,<b>324.4) = (0,0, 648.8)<br /> However, the answer I should be getting is 487<br /> <br /> Am I doing something wrong?<br /> (and why is it ignoring my LaTex tags?)</b></b></b></b></b></b></b></b></b></b></b></b></b></b></b></b><br /> </b></b></b>[/B][/itex][/itex]
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