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 unit of the constant of proportionality, we need to analyze the given quantities and their SI units.
The current density Jx is given in units of A/m², which represents the amount of current passing through a unit area of the material.
The magnetic field Bz is given in units of Tesla (T), which measures the strength of the magnetic field.
The electric field Ey is directly proportional to both Jx and Bz. Mathematically, we can express this relationship as:
Ey ∝ Jx * Bz
To find the unit of the constant of proportionality, we can rearrange the equation:
Ey = k * Jx * Bz
Where k is the constant of proportionality.
Now, let's analyze the units on both sides of the equation:
Ey has SI unit volts per meter (V/m).
Jx has SI unit amperes per square meter (A/m²).
Bz has SI unit Tesla (T).
Using the units of V/m, A/m², and T, we can determine the unit of k:
(V/m) = k * (A/m²) * T
Simplifying the equation, we can cancel out the units:
1 = k * (A/m) * m²
1 = k * A * m
Now, we need to find the SI unit of k. From the equation above, we can see that the unit of k is m³/As.
Therefore, the correct answer is option 4: m³/As.