Recent experiments show that $Deltagamma$, an observable designed for detecting the chiral magnetic effect (CME), in small collision system $p+A$ is similar with that in heavy ion collision $A+A$. This brings a challenge to the existence of CME because it is believed that there is no azimuthal correlation between the orientation of the magnetic field ($Phi_B$) and the participant plane ($Phi_2$) in small collision system. In this work, we introduce three charge density models to describe the inner charge distributions of proton and neutron, and calculate the electric and magnetic fields produced in small $p+A$ collisions at both RHIC and LHC energies. Our results show that the contribution of the single projectile proton to the magnetic field is the main source after average over all participants. The azimuthal correlation between $Phi_B$ and $Phi_2$ is small but not vanished. And due to the huge fluctuation of fields strength, the magnetic-field contribution to $Deltagamma$ could be large.
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