Question

A device uses hall effect to measure magnetic fields. When in a magnetic field of $200\text{G},$ it gives a hall voltage of $16\mu \text{V}.$ If with the same current and orientation, it gives a hall voltage of $23\mu \text{V}$ in an unknown field, then the magnitude of unknown field is

• A. $28.8\text{G}$
• B. $0.288\text{G}$
• C. $288\text{G}$
• D. $2.88\text{G}$

Answer 1

The correct option is C $288\text{G}$

Hall voltage is given by,
$$V_H=\frac{BI}{nqt}.....\left(1\right)$$Where,
$I=\text{current}B=\text{magnetic field}n=\text{carrier charge density}q=\text{charge}t=\text{thickness}$

As per the statement, the variables are $B\&V_H$ so that, other terms can be treated as constants.

From $\left(1\right)$ we can say that,

$V_H\propto B$

$\therefore \frac{(V_H{)}_1}{B_1}=\frac{(V_H{)}_2}{B_2}$

$\Rightarrow \frac{16\times {10}^{-6}}{200}=\frac{23\times {10}^{-6}}{B_2}$

$\therefore B_2=287.5\text{G}\approx 288\text{G}$

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, option (c) is the correct answer.

Why this question ? Considering the expression for the Hall voltage and the variables given in the statement, we establish the fact that $V_H$ and $B$ must have a directly proportional relation while the remaining quantities are constant.