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10 November, 21:58

A conducting spherical shell having an inner radius of 3 cm and outer radius of 4.3 cm carries a net charge of 9.6 μC. A conducting sphere is placed at the center of this shell hav - ing a radius of 0.8 cm and carries a net charge of 1.7 μC. Determine the surface charge density on the outer surface of the shell.

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  1. 10 November, 22:15
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    sigma = 3.4*10^-4 C / m^2

    Explanation:

    Given:

    - The net charge of the conducting sphere Q_s = 1.7 uC

    - The net charge in the shell Q_shell = 9.6 uC

    - Outer radius of the shell r = 4.3 cm

    Find:

    Determine the surface charge density on the outer surface of the shell.

    Solution:

    - The concept here is that the net charge on the conducting sphere must be equal to charge on inner shell. Hence, Q_s = Q_in

    Q_shell = Q_in + Q_out

    Q_out = Q_shell - Q_in

    Q_out = 9.6 - 1.7 = 7.9 uC

    - Now we can calculate the charge density of the outer shell by:

    sigma = Q_out / A_out

    sigma = (7.9*10^-6) / 4*pi * (0.043) ^2

    sigma = 3.4*10^-4 C / m^2
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