Consider two widely separated conducting spheres, 1 and 2, the second having twi

Question

Consider two widely separated conducting spheres, 1 and 2, the second having twice the diameter of the first. The smaller sphere initially has a positive charge q = 8.00×10-6 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.

q1?

q2?

What is the ratio of the final surface charge density of sphere 1 to that of sphere 2?

Explanation / Answer

The charges will distribute equally

q1 = q1 = q/2 = 8 x 10^-6/2 = 4 x 10^-6 C

V1 = kq1/r1

V2 = kq2/(2r1)

V1/V2 = kq1/r1 x 2r1/kq2

V1/V2 = 2

V1 = 2V2

Hence, V1 = 2V2

and q1 = q2 = 4 x 10^-6 C

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