Two small identical conducting spheres are placed with their centers a distance

Question

Two small identical conducting spheres are placed with their centers a distance d = 0.33 m apart. One is given a charge of Q1 = -20.0 x 10-9 C, and the other is given a charge of Q2 = 20.0 x 10-9 C.

a) Determine the electric force exerted on one sphere by the other. Answer in units of Newtons, and indicate by a positive value if the force is repulsive or a negative value if the force is attractive.

b) What would be the new force if their centers are now separated by a distance equal to 2 x d?

c)  What would be the new force if their centers are separated by d but Q1 was changed by 2 x Q1?

Explanation / Answer

F = Kq1q2/r^2

K = 9 x 10^9 Nm^2/C^2

F = 9x10^9x-20x19^-9x20x01^9/0.33^2

F = -3.306x10^-5 N

Force is attractive

b) F is propotional to 1/r^2

if we double the distance then force should be 1/4th of original force

F1/F2 = r2^2/r1^2

r1 = d , r2 = 2d

F1/F2 = 4d^2/d^2

F2 = F1/4

F2 = -8.265 x 10^-6 N

c) if we change one charge by 2 then new force should be 2F

Fnew = 2 x -3.306x10^-5 = -6.612 x 10^-5 N

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