Question:
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.
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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This is the Hall coefficient \(R_H = E_y/(J_xB_z) = 1/(ne)\).
Updated On: Nov 4, 2026
- \(\frac{m^2}{A}\)
- \(\frac{m^3}{As}\)
- \(\frac{m^2}{As}\)
- \(\frac{As}{m^3}\)
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The Correct Option is B
Solution and Explanation
\(E_y = R_H J_x B_z \Rightarrow R_H = \dfrac{E_y}{J_x B_z}\).
Units: \(E = \mathrm{N/C} = \mathrm{N/(A\,s)}\); \(J = \mathrm{A/m^2}\); \(B = \mathrm{N/(A\,m)}\), so \(JB = \mathrm{N/m^3}\).
\(R_H = \dfrac{\mathrm{N/(A\,s)}}{\mathrm{N/m^3}} = \dfrac{m^3}{A\,s}\).
Answer: (2) \(\dfrac{m^3}{As}\)
Units: \(E = \mathrm{N/C} = \mathrm{N/(A\,s)}\); \(J = \mathrm{A/m^2}\); \(B = \mathrm{N/(A\,m)}\), so \(JB = \mathrm{N/m^3}\).
\(R_H = \dfrac{\mathrm{N/(A\,s)}}{\mathrm{N/m^3}} = \dfrac{m^3}{A\,s}\).
Answer: (2) \(\dfrac{m^3}{As}\)
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