Fig. 4.

Test of the scaling relation: $\tau =nmB\lambda \left(R,B\right)R^2$, where $\tau$ is the generated torque, $n~10^{17}$ bact m${}^{-3}$ is the bacteria density, $m~10^{-16}$ J T${}^{-1}$ is the magnetic moment of a single bacterium, $B$ is the magnetic field intensity and $\lambda \left(R,B\right)$ is a typical length inherent to the torque generation. a ${⟨\lambda ⟩}_B$ (resp. ${⟨\lambda ⟩}_R$) is the average value of $\lambda$ with respect to $B$ (resp. $R$). We only included the data corresponding to ${\tau }_v>0.1\mathrm{nN}\mathrm{\mu }{\mathrm{m}}^{-2}$, for which the torque is strong enough to be measured out from experimental noise. The error bars are the standard deviations of the average data. This graph shows that $\lambda =8\pm 2$ µm is an intrinsic length of the system which does not depend on $R$ nor $B$. The error bars are the standard errors. b Qualitative interpretation of the rotary motor self-organization. The volume of the recirculating bacteria contributing to the torque is dimensionally $\mathcal{V}~\lambda R^2$. The picture is similar close to the south pole of the droplet