SSM A spherical conducting shell has a charge of -14 μC on its outer surface and a charged parti

step 1 Okay, so for this problem, you're given that you have a sphere, and it's a metal sphere, and it'

SSM A spherical conducting shell has a charge of -14 μC on...

SSM A spherical conducting shell has a charge of $-14 \mu C$ on
its outer surface and a charged particle in its hollow. If the net
charge on the shell is $-10 \mu C,$ what is the charge (a) on the inner
surface of the shell and (b) of the particle?

Key Concepts

Electrostatic Induction

Electrostatic induction is the process by which a charged object causes a redistribution of charges in a nearby conductor. In such situations, the conductor develops regions of opposite charge in response to the external field, and the induced charge on its inner surface exactly counterbalances the influence of the interior charge to maintain electrostatic equilibrium.

Gauss's Law

Gauss's Law relates the electric flux through a closed surface to the net charge enclosed by that surface. In conductors, this principle is used to determine that the electric field within the conducting material is zero when in electrostatic equilibrium, implying that any charge inside a hollow space must induce an equal and opposite charge on the interior surface.

Charge Distribution on Conductors

In a conductor under electrostatic conditions, excess charges reside entirely on the surfaces. The distribution of these charges is such that the net electric field inside the conductor is zero. This includes the partitioning of charges between the inner surface induced by an internal charge and the outer surface, where any additional net charge resides.

Conservation of Charge

The conservation of charge principle states that the total charge of an isolated system remains constant. When analyzing a system like a conductor with multiple surfaces, the sum of the induced charges on all surfaces must equal the total charge originally present on the conductor, ensuring that no charge is lost or created.

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