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25 March, 04:21

Sphere 1 with radius R_1 has positive charge q, Sphere 2 with radius 4.50 R_1 is far from sphere 1 and initially uncharged. The separated spheres are then connected with a wire then uncouth to retain only negligible charge. (a) What is the ratio V_1/V_2 of the final potentials of the spheres? (b) what fraction of q ends up on sphere? (c) What fraction of q ends up on sphere 2? (d) What is the ratio q_1/q_2 of the surface charge densities of the spheres?

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  1. 25 March, 04:40
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    capacitance of sphere 2 will be 4.5 times sphere 1

    a) when spheres are in contact they will have same potential finally. So

    V_1 / V_2 = 1

    b)

    Charge will be distributed in the ratio of their capacity

    charge on sphere1 = q x 1 / (1 + 4.5)

    = q / 5.5

    fraction = 1 / 5.5

    c) charge on sphere 2

    = q x 4.5 / 5.5

    fraction = 4.5 / 5.5

    d) surface charge density of sphere 1

    = q / (5.5 x A) where A is surface area

    surface charge density of sphere 2

    = q x 4.5 / (5.5 x 4.5² A) where A is surface area

    = q / (5.5 x 4.5 A)

    q_1/q_2 = 4.5
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