(8e24p64) Consider two widely separated conducting spheres, 1 and 2, the second

Question

(8e24p64) Consider two widely separated conducting spheres, 1 and 2, the second having four times the diameter of the first. The smaller sphere initially has a positive charge q 6.00x106 C, and the larger one is initially uncharged. You now connect the spheres with a long thin wire. How are the final potentials V1 and V2 of the spheres related? Find the final charges q1 and q2 91? Submit Answer Incorrect. Tries 1/99 Previous Tries q2? Submit Answer Tries 0/99 What is the ratio of the final surface charge density of sphere 1 to that of sphere 2? Submit Answer Tries 0/99

Explanation / Answer

as sphere are connected with wire,

so both sphere will have same potential across wire.

V1= V2

k q1 / r1 = k q2 /r2

and r2 = 4 r1

q2 = 4 q1 ..... (i)

and q1 + q2 = q = 6 x 10^-6

4 q1 + q1 = 6 x 10^-6

q1 = 1.2 x 10^-6 C .........Ans

q2 = 4 q1 = 4.8 x 10^-6 C .....Ans

sigma = q / (4 pi r^2)

ratio = q1 r2^2 / q2 r1^2

= (q1 16 r1^2)/(4 q1 r1^2)

= 4 .......Ans

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