We extend the topological particle framework of Discrete Topological Torsion Theory (DTTT), in which fundamental particles are knotted solitons in a Cosserat elastic vacuum, to derive the electromagnetic properties of the electron and neutron. Our central result is a theorem showing that fractional electric charges emerge necessarily from the torus knot parameters: for the trefoil T(2,3), the q=3 meridional winding quantises charge in units of e/3 while the isospin doublet constraint uniquely selects the lobe charges +2e/3, -e/3—precisely the quark model values, derived here without reference to quarks or QCD. The electron, classified as an unknot (nT=0), has no topologically stabilised charge radius, consistent with experimental bounds re<10−18 m. For the neutron, the trilobular charge asymmetry yields ⟨rE2⟩n<0 with the correct sign. We introduce the Sachs-Dirac-Foldy decomposition to separate the model-independent Foldy contribution (+0.0633fm2) from the intrinsic Dirac radius (−0.1794fm2). A breathing-mode conjecture yields ⟨r12⟩n=−nTλp2=−0.176 fm2, within 2% of the experimental value −0.172 fm2.