Question

A conductor of mass $m$ and length $l$ is placed perpendicular to a horizontal uniform magnetic field $B$. Suddenly, a certain amount of charge is passed through it, and it is found to jump to a height $h$. The amount of charge that passes through the conductor is -

• A. $\frac{m\sqrt{gh}}{Bl}$
• B. $\frac{2m\sqrt{gh}}{Bl}$
• C. $\frac{m\sqrt{2gh}}{Bl}$
• D. None of these

Answer 1

The correct option is C $\frac{m\sqrt{2gh}}{Bl}$


We know that,

Impulse $=$ Change in momentum

$F\Delta t=m\sqrt{2gh}\left\{\begin{array}{c}\because v^2=u^2+2gh\\ \text{or}{v}^2=2gh\end{array}\right\}$

$\Rightarrow BIl\Delta t=m\sqrt{2gh}[\because F=BIl]$

$\Rightarrow I\Delta t=\frac{m\sqrt{2gh}}{Bl}$

$\Rightarrow \Delta q=\frac{m\sqrt{2gh}}{Bl}\{\because I=\frac{\Delta q}{\Delta t}\}$

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