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(B) According to the Hall effect,the electric field $E_y$ is given by $E_y = R_H J_x B_z$,where $R_H$ is the Hall coefficient.The constant of proporti

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$m^3/(A \cdot s)$

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(B) According to the Hall effect,the electric field $E_y$ is given by $E_y = R_H J_x B_z$,where $R_H$ is the Hall coefficient.The constant of proportionality $K$ is $R_H = \frac{E_y}{J_x B_z}$.The $SI$ unit of $E_y$ is $V/m$ (or $N/C$).The $SI$ unit of $J_x$ is $A/m^2$.The $SI$ unit of $B_z$ is $T$ (Tesla),where $1 \ T = 1 \ (N \cdot s)/(C \cdot m) = 1 \ (N)/(A \cdot m)$.Substituting the units:$K = \frac{V/m}{(A/m^2) \cdot (N/(A \cdot m))} = \frac{V/m}{N/m^3} = \frac{V \cdot m^2}{N}$.Since $V = (J/C) = (N \cdot m)/(A \cdot s)$,we have:$K = \frac{(N \cdot m / (A \cdot s)) \cdot m^2}{N} = \frac{m^3}{A \cdot s}$.

$A$ 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:

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