Question

A $U$ tube of uniform square cross-sectional side $a$ has mercury in it. Current $I$ is passed between sealed electrodes $x$ and $y$. A magnetic field $B$ is applied across horizontal section perpendicular to the plane of diagram. The difference in mercury levels is $[$Given: $\rho =$ density of mercury$]$ :

• A. $\frac{2}{3}\frac{BI}{\rho ga}$
• B. $\frac{2BI}{\rho ga}$
• C. $\frac{BI}{\rho ga}$
• D. $\frac{4BI}{\rho ga}$

Answer 1

Answer: (C)

$\frac{BI}{\rho ga}$

The difference in mercury level between the columns is due to the force experienced by the mercury $\rho a^{2}gh$
The force experience by the mercury of length $a$ is $IaB$
Equating both forces $\rho a^{2}gh=IaB$
$\Rightarrow h=\frac{IB}{\rho ag}$