Problem 2
A capacitor is charged to voltage and then isolated. Find its charge and stored energy. Assume ideal objects and components, neglect unstated losses, and use SI units. (a) Derive the primary requested quantity from the appropriate law. (b) Analyze quantitatively how the result depends on the given parameters. (c) Check a physically meaningful limiting case and explain its meaning. State sign conventions, show reasoning, and check dimensions. (a) Calculate the requested quantity from the data. (b) Give the law or expression showing parameter dependence. (c) Examine a limit consistent with the model. While it remains isolated, a dielectric of relative permittivity kappa is inserted to fill the gap; the total charge therefore stays fixed.
problems.proof.stepOf
problems.proof.analysis
Rearrange algebraically and select the solution consistent with initial conditions and physical meaning. Check dimensions before interpreting the expression.
problems.proof.pitfall. Keep the sign convention and constraints consistent; do not replace a signed quantity by its magnitude without justification.