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

Question:

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

1. $\frac{m^{2}}{A}$

2. $\frac{m^{3}}{A s}$

3. $\frac{m^{2}}{A s}$

4. $\frac{A s}{m^{3}}$

JEE Main Previous Year Single Correct Question of JEE Main from Chemistry Laws of Motion chapter.

JEE Main Previous Year 2013

Correct Option: 2

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 $\left.J=\frac{I}{\text { Area }}\right]$

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