What charge q3 & position vector r3 be placed if Chrges q1 & q2 with posnn vctors r1 & r2 to exp. nil force? - general nil megaupload
Charges Q1 and Q2 are in the plan, is the general term for loading into Q3 with R3 vector so that the burden does not charge any q3 force.ie Q3 experince Q1 = f (, R1, Q2, R2)
R3 = g (T1, R1, Q2, R2)
Wednesday, December 16, 2009
General Nil Megaupload What Charge Q3 & Position Vector R3 Be Placed If Chrges Q1 & Q2 With Posnn Vctors R1 & R2 To Exp. Nil Force?
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Sum of forces by T1 and T2 to T3
F = 0 = kq1q3 R13 / (R13) ^ 3 + kq2q3R23 / (R23) ^ 3
where R13 Q1 = vector to Q3, R23 = vector from T2 to T3, R13 = R13 size of the order of R23 = R12
You can simplify
Q1 R13 / (R13) ^ 3 + Q2 R23 / (R23) ^ 3 = 0
However, as the vectors of the original Q1 and Q2, R1 and R2, respectively.
Then R13 = R1 - R3
R23 = R2 - R3
and R13 = sqrt (r1 ^ 2 + R3 ^ 2-2r1r3cos (A13))
r23 = sqrt (R2 + R3 ^ 2 ^ 2-2r2r3cos (A23))
R1, R2 and R3 all sizes of the vectors R1, R2 and R3 and A13 = angle between R1 and R3 and Vector A23 = angle between R2 and R3.
and the condition is without the power
Q1 R13 / (R13) ^ 3 + Q2 R23 / (R23) ^ 3 = 0
* Q1 (R1-R3) / (R1 + R3 ^ 2 ^ 2-2r1r3cos (A13)) ^ (... = Q2 * (R2 - R3) / (r2 ^ 2 + R3 ^ 2-2r2r3cos (A23)) ^ (3 / 2)
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