B. What must be the placement of the thirdcharge for the first two to be in equi
ID: 1667435 • Letter: B
Question
B. What must be the placement of the thirdcharge for the first two to be in equilibrium? Two charges, -Q0 and -3Q0 , are a distance l apart. These two charges are free to move but do not because there is a third charge nearby. A. What must be the charge of the third charge for the first two to be in equilibrium? Express your answer in terms of some or all of the variables Q0 and l. B. What must be the placement of the third charge for the first two to be in equilibrium? Express your answer in terms of some or all of the variables Q0 and l. I tried 3q^20/l^2 and (Q0/1 + 1/3)^2 and 3/(sq. root 3 + 1)^2 for part A. All of them are incorrect. I have no idea what part B is. Please help!Explanation / Answer
Refer to the -Q0 charge as Q1 and the -3Q0 charge as Q2. The repelling force F = kQ1Q2/L^2. We want to add Q3 to provide an equal attracting force to each ofQ1 and Q2. The added charge Q3 must be positive and located between Q1 andQ2. L13 = sqrt(kQ1Q3/F), L23 = sqrt(kQ2Q3/F) L13+L23 = L L13/L23 = sqrt(Q1/Q2) = sqrt(1/3) = 0.57735 L13 = L*(0.57735/1.57735) = 0.3660254L. This is answer B, given as the distance from Q1 to Q3. The analytical formula is L13 = L*sqrt(Q1/Q2)/(1+sqrt(Q1/Q2)) =L/(1+1/sqrt(Q1/Q2)). Expressed in terms specific to this problem, L13 =L/(1+1/sqrt(1/3)). A. To find Q3, we can solve L13 = sqrt(kQ1Q3/F). Q3 = L13^2*F/(kQ1) = L13^2*kQ1Q2/L^2/(kQ1) = L13^2*Q2/L^2 =0.3660254^2*Q2 = -0.1339746*3Q0 = -0.4019238*Q0. The analytical formula is Q3 = -Q2[sqrt(Q1/Q2)/(1+sqrt(Q1/Q2))]^2 =-Q1/(1+sqrt(Q1/Q2))^2. Expressed in terms specific to this problem, Q3 =Q0/(1+sqrt(1/3))^2.
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