GATE 2022 IN Q.17: solution and answer

Official answer: DSource: Official answer key, GATE 2022 IN (IIT Kharagpur)

1. A Hall sensor is a thin slab of semiconductor carrying a bias current $I$, with a magnetic flux density $B$ applied perpendicular to the current.

2. The moving charge carriers (velocity $v$) feel the magnetic force $\vec{F}=q\vec{v}\times \vec{B}$. This is the Lorentz force.

3. The force pushes the carriers toward one side of the slab. Charge builds up there until the transverse electric force $q{E}_H$ balances $qvB$.

4. The transverse Hall voltage is $V_H=\frac{R_{H}IB}{t}$, where $R_H$ is the Hall coefficient and $t$ is the slab thickness. It is proportional to $B$.

5. Compare the options. The photoelectric effect is electron emission driven by light. The Seebeck effect is a thermoelectric voltage from a temperature difference. The piezoelectric effect is charge from mechanical stress. None of these involves a magnetic field.

6. Only the Lorentz force explains the Hall voltage, so the answer is (D).