A conductor in electrostatic equilibrium has a cavity that...

A conductor in electrostatic equilibrium has a cavity that contains a point charge $q_{1}=+5 \mu \mathrm{C}$. Outside the conductor is another point charge $q_{2}=-12 \mu \mathrm{C}$. The conductor itself carries a net charge $-4 \mu \mathrm{C}$. Find the net charge on (a) the inner surface of the conductor and (b) the outer surface of the conductor.

Key Concepts

Electrostatic Equilibrium in Conductors

In electrostatic equilibrium, the electric field inside a conductor is zero and all excess charge resides on its surface. This condition forces free charges in the conductor to rearrange themselves so that any internal fields cancel. It is fundamental in determining how charges distribute, especially when external influences or internal cavities with charges are present.

Gauss's Law

Gauss's Law relates the net electric flux through a closed surface to the charge enclosed by that surface. In the context of conductors, it is often used to evaluate the induced charge on surfaces by choosing an appropriate Gaussian surface inside the conductor where the electric field is zero, thereby linking enclosed charges to the surface charge distribution.

Induced Charge and Charge Redistribution

When a charged object is placed inside a cavity of a conductor, it induces an equal and opposite charge on the cavity's inner surface. This happens so that the electric field within the bulk of the conductor remains zero. Similarly, the remaining net charge of the conductor redistributes itself on the outer surface to maintain overall charge balance.

Surface Charge Distribution on Conductors

The total net charge of a conductor is distributed between its inner and outer surfaces based on the presence of any charges inside cavities and on the conductor itself. The inner surface acquires a charge that exactly cancels the effect of any enclosed charge, while the outer surface’s charge is the algebraic sum of the conductor's net charge and the negative of the inner surface charge.

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