Question

The Hall experiment is carried out with a non-magnetic semiconductor. The current $I$ is along the X-axis and the magnetic field $B$ is along the Z-axis. Which one of the following is the CORRECT representation of the variation of the magnitude of the Hall resistivity $\rho_{xy}$ as a function of the magnetic field?

• A. $\rho_{xy}$ vs. $B$ (constant value)
• B. $\rho_{xy}$ vs. $B$ (linear increase)
• C. $\rho_{xy}$ vs. $B$ (quadratic curve)
• D. $\rho_{xy}$ vs. $B$ (step function)

Hint:

In Hall effect experiments, Hall resistivity $\rho_{xy}$ is directly proportional to the magnetic field strength for non-magnetic materials, resulting in a linear increase.

Answer 1

The Correct Option is B

In the Hall effect experiment, the Hall resistivity $\rho_{xy}$ is proportional to the magnetic field $B$ when the current flows perpendicular to the magnetic field in a non-magnetic semiconductor.
- As the magnetic field increases, the Hall resistivity $\rho_{xy}$ increases linearly. This is because the Hall voltage generated is directly proportional to the magnetic field strength, leading to a linear relationship between $\rho_{xy}$ and $B$.
Thus, the correct representation is a linear increase of $\rho_{xy}$ with $B$, as shown in option (B).