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.

Question

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. (A) (m2/A) (B) (m3/As) (C) (m2/As) (D) (As/m3)

Tardigrade Admin · Accepted Answer

According to question Ey propto Jx Bz ∴ Constant of proportionality K=(Ey/BzJx)=(C/Jx)=(m3/As) [As (E/B) =C (speed of light) and J=(I/Area)]

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.

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

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

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

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

According to question
$E_{y} \propto J_{x} B_{z}$
$∴$ Constant of proportionality
$K = \frac{E _{y}}{B _{z} J _{x}} = \frac{C}{J _{x}} = \frac{m _{3}}{A s}$
$[A s \frac{E}{B} = C (s p ee d o f l i g h t) an d J = \frac{I}{A re a}]$

Q. 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.

Am2​

Asm3​

Asm2​

m3As​