A metal sample carrying a current along $\mathrm{X-}$ axis with density $\mathrm{J}_{\mathrm{x}}$ is…
A metal sample carrying a current along $\mathrm{X-}$ axis with density $\mathrm{J}_{\mathrm{x}}$ is subjected to a magnetic field $\mathrm{B}_z$ (along $\mathrm{z-}$axis). The electric field $\mathrm{E}_{\mathrm{y}}$ developed along $\mathrm{Y}$-axis is directly proportional to $\mathrm{J}_{\mathrm{x}}$ as well as $\mathrm{B}_{\mathrm{z}}$. The constant of proportionality has SI unit.
$\frac{m^2}{A}$
$\frac{m^3}{A s}$
$\frac{m^2}{A s}$
$\frac{A s}{m^3}$
Solution
According to question
$\mathrm{E}_{\mathrm{y}} \propto \mathrm{J}_{\mathrm{x}} \mathrm{B}_{\mathrm{Z}}$
$\therefore$ Constant of proportionality
$\mathrm{K}=\frac{\mathrm{E}_{\mathrm{y}}}{\mathrm{B}_{\mathrm{Z}} \mathrm{J}_{\mathrm{x}}}=\frac{\mathrm{C}}{\mathrm{J}_{\mathrm{x}}}=\frac{\mathrm{m}^3}{\mathrm{As}}$
$\left[\right.$ As $\frac{E}{B}=C$ (speed of light) and $\left.J=\frac{I}{\text { Area }}\right]$