Problem 2
A parallel-plate capacitor of plate area and separation is connected to a constant voltage . A dielectric of relative permittivity fills a fraction of the plate length, parallel to the plates; the remainder is vacuum. Neglect edge effects. Find the capacitance, positive-plate charge, and stored field energy. (a) State the assumptions and establish the governing equation for the requested quantity. (b) Solve it in terms of the given symbols, identifying the direction, sign, or physical nature of the result. (c) Check a simple limiting case and state when the model remains valid. Use SI units consistently, retain the symbols in the setup, and enforce all geometric constraints and initial conditions.
problems.proof.stepOf
problems.proof.analysis
The dielectric and vacuum regions are side by side, share the same plate spacing , and experience the same voltage .