= Relativistic charge density of counterstreaming beams
{title2=$\lambda'=-\gamma vI/c^2$}
Two equal opposite line charge densities moving in opposite directions have zero net line charge but a nonzero total current $I$. Under a longitudinal <Lorentz boost>, the charge-current four-vector gives $\lambda'=\gamma(\lambda-vI/c^2)=-\gamma vI/c^2$. Equivalently, for lab densities $n$ and speeds $\pm u$, their separate boosted number densities are $\gamma n(1\mp vu/c^2)$. Their imbalance creates the boosted radial <electric field>, consistently with <Lorentz transformation of electromagnetic fields> and <Gauss's law>.
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