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October 24, 2014

October 24, 2014

Posted by **GT** on Wednesday, July 10, 2013 at 10:57am.

Four identical particles with mass m and charge +q, orbit a charge −q as shown in the figure. The four positive charges always form a square of side l(t) while the negative charge stays at rest at the center of the square. The motion of the charges is periodic with period T. That is, if the vectors r_k(t), k={1,2,3,4}, describe the position of the charges then we have that

r_k(t+T)=r_k(t).

It is also known that the side of the square oscillates between l_min=1/4L_0 and l_max=L_0. Determine the period T in seconds if the parameters q,m and L_0 satisfy the relation

(kq^2)/(m(L_0^3))=10^4 s^−2,where k=1/(4πϵ_0)

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