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Physics C: E&M · FRQ Trainer

Free-response 1 of 17 · Electric Charges, Fields, and Gauss’s Law

7 pts our rubric

The real Physics C: E&M Section II is 4 free-response questions in 95 minutes, 50% of your score. Four questions — mathematical routines, translation between representations, experimental design and analysis, and qualitative/quantitative translation. Point totals vary by form; the 2025 exam ran 10 / 12 / 10 / 8 for 40 raw points. This prompt is ours, written to the same skills — score it against the rubric below, not against that structure.

Prompt

A solid insulating sphere of radius R has a uniform volume charge density ρ.

aUse Gauss's Law to derive an expression for the magnitude of the electric field E(r) inside the sphere (r < R).3 pts

bDerive an expression for the electric potential V(r) at the surface of the sphere, assuming V = 0 at infinity.2 pts

cA proton (charge +e) is released from rest at the surface. Determine its kinetic energy when it reaches a distance 3R from the center.2 pts

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