We have measured magnetoresistance of suspended graphene in the Corbino geometry at magnetic fields up to $B=0.15,$T, i.e., in a regime uninfluenced by Shubnikov-de Haas oscillations. The low-temperature relative magnetotoresistance $[R(B)-R(0)]/R(0)$ amounts to $4000 B^2% $ at the Dirac point ($B$ in Tesla), with a quite weak temperature dependence below $30,$K. A decrease in the relative magnetoresistance by a factor of two is found when charge carrier density is increased to $|n| simeq 3 times 10^{-10}$ cm$^{-2}$. The gate dependence of the magnetoresistance allows us to characterize the role of scattering on long-range (Coulomb impurities, ripples) and short-range potential, as well as to separate the bulk resistance from the contact one. Furthermore, we find a shift in the position of the charge neutrality point with increasing magnetic field, which suggests that magnetic field changes the screening of Coulomb impurities around the Dirac point. The current noise of our device amounts to $10^{-23}$ A$^2$/$sqrt{textrm{Hz}}$ at $1,$kHz at $4,$K, which corresponds to a magnetic field sensitivity of $60$ nT/$sqrt{textrm{Hz}}$ in a background field of $0.15,$T.
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