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

Question

Sphere 1 with radius R_1 has positive charge q. Sphere 2 with radius R_1 is far from sphere 1 and initially un 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.) Number Units Number Units Number Units

Explanation / Answer

(a)

the charge flows from sphere1 to sphere2 ntial bothe the spheres acquire same potential

V1 equal to V2

(b)

let q charge flow from sphere 1 to sphere 2

V1 = V2

k*(q1-q)/R1 = k*q/R2

(q1-q)/R1 = q/(7R1)

q1-q = q/7

q1 = q + q/7

q1 = 8q/7

q = 7q1/8

part(b)

charge on sphere1 = q1 -q = q1 - (7/8)*q1 = (1/8)*q1    C

part(c)

charge on sphere 2 = q = (7/8)*q1   C

part(d)

charge density of sphere 1 = (q1/8)/(4*pi*R1^2)

charge density of sphere 2 = (7q1/8)/(4*pi*R2^2)

ratio = (R2/R1)^2*(1/7) = 7^2*(1/7) = 7 <<<-----answer

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