- Home
- Standard 12
- 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 io $J_x$ as well as $B_z$ . The constant of proportionality has $SI\, unit$.
$\frac{{{m^2}}}{A}$
$\frac{{{m^3}}}{As}$
$\frac{{{m^2}}}{As}$
$\frac{{As}}{{{m^3}}}$
Solution
According to question
$\mathrm{E}_{\mathrm{y}} \propto \mathrm{J}_{\mathrm{x}} \mathrm{B}_{\mathrm{Z}}$
$\therefore $ Constant of proportionality
$\mathrm{K}=\frac{\mathrm{E}_{\mathrm{y}}}{\mathrm{B}_{\mathrm{Z}} \mathrm{J}_{\mathrm{X}}}=\frac{\mathrm{C}}{\mathrm{J}_{\mathrm{X}}}=\frac{\mathrm{m}^{3}}{\mathrm{A} \mathrm{s}}$
$\left[\text { As } \frac{\mathrm{E}}{\mathrm{B}}=\mathrm{C}(\text { speed of light }) \text { and } \mathrm{J}=\frac{1}{\text { Area }}\right]$
