Read Concentric Conductors: Field, Induced Charge and Energy
For a conductor in electrostatic equilibrium, the field within its material is zero. This one fact determines induced charge on the inner surface and makes the region-by-region field simple.
Electricity questions depend on identifying charge, a conducting path and the condition that controls current or magnetic effect.
Separate charge, current and the path between them
Charge is a property · current needs a conducting path
Charge is a property; current needs a conducting path. Decide first whether the question concerns charging, resistance, current or earthing.
Work from the metal outward
Draw a Gaussian surface inside the conductor. The net enclosed charge must be zero, fixing the charge induced on the inner surface.
Then use charge conservation
The conductor's stated total charge equals inner-surface charge plus outer-surface charge. This determines the outer-surface charge.
Treat each region separately
Write E(r) for the cavity, conductor, and exterior using the charge enclosed in each region.
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- ✓Set E = 0 inside the metal.
- ✓Fix inner charge with Gauss's law.
- ✓Find outer charge from conservation.
The charge on the outer surface is not automatically the shell's original charge; account for the induced inner-surface charge first.
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