Why does Gauss’s law fail to determine the electric field for a finite charged object without symmetry?
**Gauss's theorem** states total flux through closed surface equals enclosed charge divided by free-space permittivity, Φ_total = q_enc/ε₀, ε₀ = 8.854×10⁻¹² C²/(N·m²). Result independent of shape or size, depends only on net enclosed charge, enabling charge determination from flux. Gauss’s law requires a Gaussian surface with symmetry matching the charge distribution to simplify field calculation. For finite, asymmetric objects, the field varies in complex ways, making symmetry-based simplification impossible without additional methods. Substituting values gives Lack of symmetry, which matches
Ref: NCERT > Physics Book > Electric Charges and Fields > Gauss's Theorem and Total Flux