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Spherical conducting shell, particle with a charge, potential energy, two charge system

Please show all work and show all equations used and diagrams.

1) A spherical conducting shell has charge Q. A particle with charge q is placed at the center of the cavity. The charge on the inner surface of the shell and the charge on the outer surface of the shell, respectively are:

2) A particle with a charge of 5.5*10^-6C is 3.5 cm from a particle with a charge of -2.3*10^-8C. the potential energy of this two particle system, relative to the potential energy at infinite separation is:

3) A particle with a charge of 5.5*10^-8C is fixed at the origin. A particle wth a charge of -2.3*10^-8C is moved from x=3.5cm on the x axis to y=3.5cm on the y axis. The change in potential energy of the two charge system is:

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Since the electrical field in between the inner and outer surfaces is zero, by using Gauss Law we know the total enclosed ...

Solution Summary

With calculations and narrative, the problems are answered.