Read Charged Sector Discs: Integrate Rings, Then the Angle
At a point on the symmetry axis, every area element at the same radius has the same distance to the point. A quarter disc changes only the angular range in the area integral.
Potential on the Axis of a Sector Disc is the central idea in this question pattern. Identify the condition in the stem before applying the method below.
Start with the condition
Integrate rho first, then use the sector angle π/2.
Build the governing relation
Check dimensions: sigma times a length divided by ε₀ has volts. At large z the answer should approach total charge divided by 4 π ε₀ z.
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 the full-disc result without multiplying by the quarter angular fraction gives four times the potential.
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