Electromagnetic Induction

JEE Main level, single correct, medium

62 of 153

Question 62 of 153

A metal sample carrying a current along X−\mathrm{X-} axis with density Jx\mathrm{J}_{\mathrm{x}} is subjected to a magnetic field Bz\mathrm{B}_z (along z−\mathrm{z-}axis). The electric field Ey\mathrm{E}_{\mathrm{y}} developed along Y\mathrm{Y}-axis is directly proportional to Jx\mathrm{J}_{\mathrm{x}} as well as Bz\mathrm{B}_{\mathrm{z}}. The constant of proportionality has SI unit.

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Answer: (B) m3As\frac{m^3}{A s}

According to question
Ey∝JxBZ\mathrm{E}_{\mathrm{y}} \propto \mathrm{J}_{\mathrm{x}} \mathrm{B}_{\mathrm{Z}}
∴\therefore Constant of proportionality
K=EyBZJx=CJx=m3As\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{As}}
[\left[\right. As EB=C\frac{E}{B}=C (speed of light) and J=I Area ]\left.J=\frac{I}{\text { Area }}\right]

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