Scanning-tunnelling potentiometry measurements by the Brar experimental group reveal magnetic-field-dependent voltage patterns around a circular graphene p–n junction. Motivated by this collaboration, I will discuss a related theoretical question: what determines the effective transport size of a smooth density perturbation? Our theoretical work shows that local Ohm–Hall transport can produce an effective obstacle radius R_no ~ a α^(−1/β) ≫ a, where a characterizes the perturbation, β > 2 describes its density tail, and α = σ_xx/|σ_xy| ≪ 1. This amplification arises from competition between Hall circulation and dissipative leakage, without invoking viscosity. The resulting far-field dipole also poses an inverse problem: its magnitude alone cannot separate the perturbation size, the density profile and transport coefficients, while its orientation supplies complementary information. Returning to the graphene experiment, I will discuss annular features whose separation approximately follows the cyclotron diameter, as predicted by a kinetic calculation with a specified boundary. A different question about what experiments reveal arises in correlated electron systems: can electron transfer miss the lowest charged state? Motivated by the one-third-filled charge crystal proposed for twisted MoTe₂, I studied a twelve-site, four-carrier extended Hubbard model by exact diagonalization. In this model, the lowest vacancy state retains a reversed magnetic moment up to a field about fifteen times larger than that needed to align the background. Because carrier number in each valley is conserved, removing one carrier from the aligned background cannot create this state, so it is absent from the direct removal spectrum. This raises three questions: does the reversed moment remain bound to the vacancy in larger crystals, can the charge crystal modify this binding beyond the known triangular-lattice magnetic-polaron mechanism, and can weak valley mixing make the lower state visible? A related question is whether magnetic rearrangement changes the ordering and electron-transfer weight of fractionally charged excitations in MoTe₂.