Sphere 1 with radius R_1 has positive charge q. Sphere 2 with radius 7.0/R_1 is

Question

Sphere 1 with radius R_1 has positive charge q. Sphere 2 with radius 7.0/R_1 is far from sphere 1 and initially uncharged. After the separated spheres are connected with a wire thin enough to retain only negligible charge, (a) is potential V_1 of sphere 1 greater than, less than, or equal to potential V_2 of sphere 2? What fraction of q ends up on (b) sphere 1 and (c) sphere 2? (d) What is the ratio of the final surface charge density of sphere 1 to that of sphere 2? (Answer with 2 significant figures.)

Explanation / Answer

b) potential is equal,

kq1/R1 = kq2/(7R1)

q2 = 7q1

total charge = q1+q2 = q1+7q1 = 8q1

Fraction on sphere 1 = 1/8 = 0.125

c) fraction on sphere 2 = 7/8 = 0.875

d) ratio = q1/(4pi R1^2) / [ 7q1/(4pi 49R1^2)]

        = 1/[7/49] = 7

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