13. Two free goint charges +g and +4g are a distance L apart.A.prd charge is so

Question

13. Two free goint charges +g and +4g are a distance L apart.A.prd charge is so placed thattbeentire system is in equilibrium. (a) Find the sign, magnitude, and location of the third charge. (b) Show that the equilibrium is unstable. 14. A charge Q is fixed at each of two opposite comers of a square. A charge q is placed at each of the other two corners (a) If the resultant electrical force on Q is zero, how are 2* and q relatod? (b) Couldgle chosen to make the resultant electrical force on every charge zero? Explain your answer. 15. A certain charge 2 is to be divided into two parts (Q-4) and q. What is the relation of Qtoq if the two parts, placed a given distance apart, are to have a maximum Coulomb re- pulsion? und 16. Two similar tiny balls of mass m are hung from silk threads of length L and carry oqual charges q as in Fig. 14. Assume that is so small that tan can be replaced by its approxi- mate equal, sin 0, (a) To this approximation show that, for equilibrium nd to 2neomg where x is the separation between the balls. (b) If L-122cm, m-11.2g, and x-4.70 cm, what is the value of q? mpo- d am Figure 14 Problems 16, 17, and 18 17. If the balls of Fig. 14 are conducting, (a) what happens to them after one is dischangedt Finl

Explanation / Answer

15

a = distance between the charges

Q = one charge

Q - q = other charge

force between the charges is given as

F = k Q (Q - q)/a2

F = k (Q2 - Q q)/a2

taking derivative both side relative to Q

dF/dQ = (2Q - q) (k/a2)

for maximum force

dF/dQ = 0

(2Q - q) (k/a2) = 0

2Q = q

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