Finding the Electric Field as a Result of Two Point Charges

[Jefferson]

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

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 /> (0,0,8)[&lt;b&gt;/itex]&lt;/b&gt;:&lt;br /&gt; (0,0,8) - (0,0,4) = (0,0,4)&lt;b&gt;&lt;br /&gt; &lt;/b&gt;(0,0,8) - (0,0,-4) = (0,0,12)&lt;b&gt;&lt;br /&gt; \frac{ k_e&lt;/b&gt;&amp;lt;b&amp;gt;−3 \mu C (0,0,4) }{ 4^3} + &amp;lt;b&amp;gt;\frac{ &amp;lt;b&amp;gt;k_e&amp;lt;/b&amp;gt; &amp;lt;b&amp;gt;3 \mu C (0,0,12) }{ 12^3 }&amp;lt;/b&amp;gt;&amp;lt;/b&amp;gt;&amp;lt;/b&amp;gt;&lt;b&gt;&lt;b&gt;&lt;b&gt;&lt;br /&gt; &lt;br /&gt; -1685.625 + 187.29166 = -1498.33334&lt;br /&gt; However, the answer I should be getting (apparently) is 609&lt;br /&gt; &lt;br /&gt; (4,4,0):&lt;br /&gt; &lt;b&gt;&lt;b&gt;(4,4,0) &lt;/b&gt;- (0,0,4) = (4,4,-4)&lt;br /&gt; &lt;b&gt;(4,4,0)&lt;/b&gt; - (0,0,-4) = (4,4,4)&lt;br /&gt; &lt;br /&gt; &lt;b&gt;k&lt;sub&gt;e&lt;/sub&gt; &lt;b&gt;−3 µC (4,4,-4) / (4^2 + 4^2 + 4^2)^(3/2) + &lt;b&gt;k&lt;sub&gt;e&lt;/sub&gt; &lt;b&gt;3 µC &lt;b&gt;(4,4,4) / (4^2 + 4^2 + 4^2)^(3/2)&lt;br /&gt; &lt;br /&gt; &lt;b&gt;k&lt;sub&gt;e&lt;/sub&gt; &lt;b&gt;−3 µC (4,4,-4) / (48)^(3/2) + &lt;b&gt;k&lt;sub&gt;e&lt;/sub&gt; &lt;b&gt;3 µC &lt;b&gt;(4,4,4) / (48)^(3/2)&lt;br /&gt; &lt;br /&gt; (-324.4, -&lt;b&gt;324.4, &lt;b&gt;324.4) + (&lt;b&gt;324.4,&lt;b&gt;324.4,&lt;b&gt;324.4) = (0,0, 648.8)&lt;br /&gt; However, the answer I should be getting is 487&lt;br /&gt; &lt;br /&gt; Am I doing something wrong?&lt;br /&gt; (and why is it ignoring my LaTex tags?)&lt;/b&gt;&lt;/b&gt;&lt;/b&gt;&lt;/b&gt;&lt;/b&gt;&lt;/b&gt;&lt;/b&gt;&lt;/b&gt;&lt;/b&gt;&lt;/b&gt;&lt;/b&gt;&lt;/b&gt;&lt;/b&gt;&lt;/b&gt;&lt;/b&gt;&lt;/b&gt;&lt;br /&gt; &lt;/b&gt;&lt;/b&gt;&lt;/b&gt;[/B]

 

[Jefferson]

Oops, sorry, didn't mean to double post.