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
I=j(x)A
evB(z) =eE(y)
E(y)=vB(z)
neAv =j(x)A
E(y) = j(x)B(z)/ne
Constant of proportionality (Hall coefficient) = 1/ne=m³/C = m³/A•s
To determine the SI unit of the constant of proportionality, let's consider the given information. We have a metal sample carrying current along the X-axis with current density Jx, and it is subjected to a magnetic field Bz along the Z-axis. The resulting electric field developed along the Y-axis, Ey, is directly proportional to both Jx and Bz.
Mathematically, we can express this relationship as:
Ey ∝ Jx * Bz
According to the given information, the constant of proportionality between Ey, Jx, and Bz has an SI unit. To find this unit, we can rearrange the equation as follows:
Ey = k * Jx * Bz
Here, k represents the constant of proportionality.
Looking at the equation, the units of Ey are determined by the units of Jx and Bz.
The SI unit for current density Jx is Ampere per square meter (A/m²).
The SI unit for magnetic field Bz is Tesla (T).
So, the unit of Ey will be the product of the units of Jx and Bz, which is (A/m²) * T.
To simplify this unit, we can rearrange it as:
(A * T) / (m²)
Thus, the SI unit of the constant of proportionality is m²/As.
Therefore, the correct answer is 1. m²/As.
The SI unit of the constant of proportionality between the electric field Ey and the current density Jx as well as the magnetic field Bz can be determined by analyzing the given information.
Let's denote the constant of proportionality as K. According to the statement, Ey is directly proportional to both Jx and Bz. Therefore, we can write the equation as:
Ey = K * Jx * Bz
Comparing the units on both sides of the equation, we can determine the SI unit of K.
The unit of electric field Ey is volts per meter (V/m). The unit of current density Jx is amperes per square meter (A/m²), and the unit of magnetic field Bz is teslas (T).
Therefore, the unit of K can be calculated as follows:
V/m = K * (A/m²) * T
Rearranging the equation, we have:
K = V / (A/m² * T)
Since V is volts (V), A/m² is amperes per square meter (A/m²), and T is teslas (T), the SI unit for K can be expressed as m²/As (option 1).