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Physics problems that have been checked.

FeynGeist writes practice problems and verifies every step symbolically and numerically — before the problem reaches you.

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Sample problem, generated as shown

An electron enters a parallel-plate capacitor at its midline with v₀ = 4.0 · 10⁷ m/s. The plates are L = 8.0 cm long, separated by d = 1.2 cm, and held at a voltage of U = 120 V. How far is the electron deflected by the end of the plates?

Solution

  1. 1Time of flight between the platest=Lv0t = \frac{L}{v_{0}}
  2. 2Transverse acceleration in the fielda=e Um da = \frac{e\,U}{m\,d}
  3. 3Deflection at the end of the platesy=12 a t2=e U L22 m d v02y = \tfrac{1}{2}\,a\,t^{2} = \frac{e\,U\,L^{2}}{2\,m\,d\,v_{0}^{2}}

Result

y≈3,5 mmy \approx 3{,}5\ \text{mm}

Verification

  • Symbolic equivalence step 1 → 2 — passed
  • Symbolic equivalence step 2 → 3 — passed
  • Numerical sample (n = 200) — passed
  • Units consistent — passed
  • Boundary condition y < d/2 — electron exits the capacitor — passed
  • Verified

How it works

  1. 1

    Choose your parameters

    Set the topic, difficulty and problem type. If you need something specific, add a sentence in the free-text field.

  2. 2

    The model proposes

    A language model writes the problem and a complete solution — step by step, not just the final answer.

  3. 3

    The verification core checks

    Every step is recomputed symbolically, and the formula is additionally tested against random values. If a step fails, the problem is discarded.

Why verification matters

A language model can phrase a problem entirely plausibly and still get the arithmetic wrong. The tricky part: you cannot tell by looking. A sign error in step three reads just as confidently as the correct calculation.

So FeynGeist separates the two. The model proposes, the mathematics decides. A computer algebra system recomputes every step symbolically; a numerical sample additionally tests the formula against concrete numbers.

Whatever fails is not flagged — it is discarded. You never see it in the first place.

The first 20 problems are free.

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