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#symmetry

2 public questions tagged with this topic.

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

Echinoderms show secondary radial symmetry because

Echinoderm adults possess pentaradial symmetry yet originate from bilaterally symmetrical ancestors, making their radial condition secondary. Planktonic larvae like bipinnaria, auricularia and dipleurula show bilateral organization with distinct anterior-posterior axis, mouth, anus and paired ciliary bands for feeding and locomotion. During metamorphosis, the left side proliferates, larval tissues are resorbed, and the adult rudiment reorganizes around oral-aboral axis into five radii. This dramatic ontogenetic transition from bilateral larva to radial adult demonstrates secondary acquisition,

Ref: Campbell Biology, 12th ed., Chapter 33: Deuterostomes – Echinodermata, NCBI Bookshelf, Invertebrate Zoology