Two small, identical conducting spheres A and B are a distance R apart; each car

Question

Two small, identical conducting spheres A and B are a distance R apart; each carries the same charge Q. What is the magnitude of the force sphere B exerts on sphere A? What is the direction of the force sphere B exerts on sphere A? An identical sphere with zero charge, sphere C, makes contact with sphere B and is then moved very far away. What is the magnitude of the net force now acting on sphere A? Express your answer in terms of the variables Q, R, and appropriate constants. Sphere C is brought back and now makes contact with sphere A and is then moved far away. What is the magnitude of the force on sphere A in this third case? Express your answer in terms of the variables Q, R, and appropriate constants

Explanation / Answer

A) use coulomb's law

F = k Q1 Q2/R^2 where k is a constant ( = 1/4 pi epsilon0)

since Q1 = Q2, F = k Q^2/R^2

B) if C is also conducting, it will take half the charge of B, so that the charge on B is now Q/2; if C moves very far away, it exerts no force on A, so the force on A now is

F = k Q/2 *Q/R^2 = k Q^2/2R^2 or half the charge in A

C) C has a charge of Q/2 before touching A; after contact, they each have a charge of 3/4Q

the force on A now is

F = k (Q/2)(3Q/4)/R^2 = 3/8 kQ^2/R^2 or 3/8 of the original force

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