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When charge is distributed continuously, the field is found by integrating contributions from infinitesimal elements: dE = k*dq/r^2. Three density types describe the distribution: linear density lambda (C/m) for wires, surface density sigma (C/m^2) for sheets, and volume density rho (C/m^3) for solid objects.

Important standard results that must be memorized for JEE:

Uniformly charged ring (charge Q, radius R) on axis at distance x: E = kQx/(x^2 + R^2)^(3/2). At center (x=0): E = 0. Maximum field at x = R/sqrt(2): E_max = 2kQ/(3*sqrt(3)*R^2). For x >> R: E ~ kQ/x^2 (point charge behavior).

Infinite line charge (lambda): E = lambda/(2piepsilon_0r) = 2klambda/r, radially outward. Falls as 1/r.

Infinite plane sheet (sigma): E = sigma/(2*epsilon_0), uniform, perpendicular to surface. Independent of distance.

Two parallel infinite sheets with equal and opposite charges (+sigma, -sigma): E = sigma/epsilon_0 between them (uniform), E = 0 outside. This is the parallel plate capacitor configuration.

Uniformly charged solid sphere (Q, radius R): Outside (r >= R): E = kQ/r^2. Inside (r < R): E = kQr/R^3 = rhor/(3epsilon_0). The field increases linearly inside and decreases as 1/r^2 outside, with maximum at the surface.

Uniformly charged disk on axis at distance x: E = (sigma/2*epsilon_0)[1 - x/sqrt(x^2 + R^2)].

The strategy for integration problems: identify the symmetry axis, decompose dE into components, note which components cancel by symmetry, and integrate only the surviving component. Always verify limits: does the result reduce to known cases (point charge at large distance, infinite sheet for large radius)?