Physics

# 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.

$\dfrac{m^{3}}{As}$

##### SOLUTION
Given: $E_{y} \alpha J_{x}$  and $E_{y} \alpha B_{Z}$
$E_{y} \alpha J_{x}B_{Z}$
$\Rightarrow E_{y}=KJ_{x}B_{Z}$ (Where K = constant of proportionality)
By Dimensional analysis we have;
$\left [ E_{y} \right ] = [KJ_{x}B_{Z}]$
$\Rightarrow \left [ K \right ] = \dfrac{\left [ E_{y} \right ]}{\left [ J_{x}B_{Z} \right ]}=\dfrac{[]M^{1}L^{1}T^{3}A^{-1}]}{[L^{-2}A^{A}][M^{1}T^{-2}A^{-1}]}$
$\Rightarrow [K]=\dfrac{[L^{3}]}{[A^{1}T^{1}]}\rightarrow$ Dimensional formual of K
So, S.I unit of K will be : $\dfrac{m^{3}}{As}$

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Single Correct Medium Published on 18th 08, 2020
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