Read Spherical Capacitors: Locate Where the Energy Lives
Capacitor energy is stored in the electric field, so find the field first and integrate its energy density over space.
Energy in a Spherical Capacitor is the central idea in this question pattern. Identify the condition in the stem before applying the method below.
Start with the condition
Between concentric shells E is proportional to 1/r². Use energy density one-half ε₀ E² and the spherical shell volume element 4 π r² dr.
Build the governing relation
For a stated fraction of total energy, integrate from the inner radius to r and divide by the complete integral from a to b.
Finish with a physical check
Check the limiting case before selecting an option: remove the special feature in the diagram or make the relevant parameter very large or very small. The result should reduce to a familiar relation.
OlympIQ exam lens
- ✓State the physical condition before choosing a formula.
- ✓Keep direction, sign and constraint information explicit.
- ✓Test one limiting case before committing to an option.
Using a uniform-field capacitor formula ignores the radial change of field in a spherical geometry.
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