a metal sample carrying a current along X-axis with density Jx is subjected to a magnetis field Bz(along z-axis). the electric field Ey developed along Y-axis is directly proportional to Jx as well as Bz. the constant of propotionality has SI unit.
1. m²/As
2. m²/A
3.As/m³
4. m³/As
To find the SI unit of the constant of proportionality between the electric field Ey and the current density Jx and magnetic field Bz, let's analyze the given information.
We know that the electric field Ey is directly proportional to both Jx and Bz. Mathematically, we can represent this as:
Ey ∝ Jx * Bz
To determine the SI unit of the constant of proportionality, we need to express the units for each quantity involved.
1. The current density Jx is given in units of Amperes per square meter (A/m²).
2. The magnetic field Bz is given in units of Tesla (T).
Using the formula for electric field (E = F/q), where F represents the force and q represents the charge, we find that the SI unit for the electric field is volts per meter (V/m).
Since Ey is directly proportional to Jx * Bz, the units for Ey must be m² * A/m² * T = m² * T.
Therefore, the SI unit of the constant of proportionality between Ey, Jx, and Bz is m²/T.
None of the given options match this unit exactly, so the correct answer may not be among the given options.