2. If the hall resistance and the magnetic field are known, we extract the charge density using $R_{xy} = -\frac{B}{ne}$. As $V_x = -\frac{I_x}{ne}B$, a stronger field yields a larger Hall voltage, making it easier to measure. Likewise, a lower charge density yields a larger Hall voltage, making it easier to measure.
3. The resistance is
3. The longitudinal resistance is
$$
R_{xx} = \frac{\rho_{xx}L}{W}
$$
where $\rho_{xx} = \frac{m_e}{ne^2\tau}$ is the longitudinal Drude resistivity. Therefore, knowing the electron density $n$, we can extract the scattering time ($\tau$). We observe that $R_{xx}$ depends on the sample geometry ($L$ and $W$, which is in contrast with the Hall resistance $R_{xy}$.
with $\rho_{xx} = \frac{m_e}{ne^2\tau}$ the longitudinal Drude resistivity. Therefore, knowing the electron density $n$, we can extract the scattering time ($\tau$). We observe that $R_{xx}$ depends on the sample geometry ($L$ and $W$), whereas the Hall resistance $R_{xy}$ does not.
