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Unformatted text preview: 49. We consider pairs of diametrically opposed charges. The net ﬁeld due to just the charges in the one
o’clock (−q ) and seven o’clock (−7q ) positions is clearly equivalent to that of a single −6q charge sitting
at the seven o’clock position. Similarly, the net ﬁeld due to just the charges in the six o’clock (−6q ) and
twelve o’clock (−12q ) positions is the same as that due to a single −6q charge sitting at the twelve o’clock
position. Continuing with this line of reasoning, we see that there are six equal-magnitude electric ﬁeld
vectors pointing at the seven o’clock, eight o’clock . . . twelve o’clock positions. Thus, the resultant ﬁeld
of all of these points, by symmetry, is directed toward the position midway between seven and twelve
o’clock. Therefore, Eresultant points towards the nine-thirty position. ...
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