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Several capacitor problem types recur in JEE with specific solution strategies.

Partially filled dielectrics: Model as series (layers perpendicular to E) or parallel (sections dividing plate area). For series with thicknesses $t_i$ and constants $K_i$: C = $epsilon_0$A / $\frac{sum of t_i}{K_i}$. For parallel with areas $A_i$: C = sum of $K_i$$epsilon_0$*$A_i$/d.

Conducting slab insertion: Equivalent to reducing the gap by the slab thickness. C = $epsilon_0$*$\frac{A}{d-t}$. If the slab touches one plate, it effectively moves that plate.

Force on dielectric (battery on): F = (K-1)*$epsilon_0$wV^$\frac{2}{2d}$, constant, directed inward. This can be derived from F = $\frac{dU}{dx}$ (keeping V constant and accounting for battery work).

Capacitor with varying separation: If plates are not parallel (wedge-shaped gap), divide into infinitesimal parallel strips and integrate. This creates a non-uniform capacitor.

Spherical shell problems: For concentric shells with charges, find the potential at each shell by summing contributions from all shells. Grounding a shell sets its potential to zero, which determines the charge redistribution.

Connected spheres: When two conducting spheres are connected by a wire, charge flows until both reach equal potential (V = $\frac{kQ}{R}$). Charge distributes in proportion to radii: Q proportional to R. Surface charge density sigma is inversely proportional to R — smaller spheres have higher sigma and higher E at the surface.