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  4. A metal sample carrying a current along X-axis with density Jx is subjected to a magnetic field Bz (along z-axis). The electric field Ey developed along Y-axis is directly proportional to Jx as well as Bz. The constant of proportionality has SI unit.

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Q. A metal sample carrying a current along $X$-axis with density $J_{x}$ is subjected to a magnetic field $B_{z}$ (along z-axis). The electric field $E_{y}$ developed along $Y$-axis is directly proportional to $J_{x}$ as well as $B_{z}.$ The constant of proportionality has SI unit.

JEE MainJEE Main 2013Physical World, Units and Measurements

Solution:

According to question
$E_{y} \propto J_{x} B_{z}$
$\therefore $ Constant of proportionality
$K=\frac{E_{y}}{B_{z}J_{x}}=\frac{C}{J_{x}}=\frac{m_{3}}{As}$
$\left[As \frac{E}{B} =C \left(speed \, of \,light\right) and \, J=\frac{I}{Area}\right] $