A metal sample carrying a current along X-axis with density Jx is… | JEE Main 2013 (25 Apr, Shift 1)

Q75JEE Main 2013 · 25 APR · SHIFT 1Medium

Applications of Dimensional Analysis

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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Answer: (b)

$E_y = R\,J_xB_z$ , so $R = \dfrac{E}{JB}$ .
Units: $E$ in V/m $=$ kg m s $^{-3}$ A $^{-1}$ , $J$ in A m $^{-2}$ , $B$ in T $=$ kg s $^{-2}$ A $^{-1}$ .
$JB$ = kg m $^{-2}$ s $^{-2}$ , so $R$ = $\dfrac{\text{kg m s}^{-3}\text{A}^{-1}}{\text{kg m}^{-2}\text{s}^{-2}} =$ m $^3$ s $^{-1}$ A $^{-1}$ .
So the answer is (b) $\dfrac{m^3}{As}$ .

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Applications of Dimensional Analysis question from JEE Main 2013 (25 Apr, Shift 1)

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