The unit of Hall Coefficient is

Question

Accepted Answer

The Hall Coefficient is a parameter that characterizes the Hall effect in a material. It is defined as the ratio of the induced electric field to the product of the current density and the applied magnetic field. The formula for the Hall Coefficient $ R_H $ is given by:

$$ R_H = \frac{E}{jB} $$

where:
- $ E $ is the electric field (measured in volts per meter, $ V/m $),
- $ j $ is the current density (measured in amperes per square meter, $ A/m^2 $),
- $ B $ is the magnetic field (measured in webers per square meter, $ wb/m^2 $).

To find the unit of the Hall Coefficient, we rearrange the formula to express $ R_H $ in terms of its units:

$$ R_H = \frac{V/m}{A/m^2 \cdot wb/m^2} $$

Simplifying the units, we get:

$$ R_H = \frac{V \cdot m^2}{A \cdot wb} $$

This matches the unit given in Option 1: $ V~m^{3}A^{-1}wb^{-1} $. Therefore, Option 1 is correct.

Now, let's explain why the other options are incorrect:

2. **Option 2: $ V~m^{2}Awb^{-1} $**

This option suggests a unit of $ V \cdot m^2 \cdot A \cdot wb^{-1} $. However, this does not match the derived unit for the Hall Coefficient, which should have $ A^{-1} $ instead of $ A $.

3. **Option 3: $ Vm^{3}A^{+1}wb^{-1} $**

This option suggests a unit of $ V \cdot m^3 \cdot A \cdot wb^{-1} $. The presence of $ A^{+1} $ instead of $ A^{-1} $ makes this option incorrect, as it does not match the derived unit for the Hall Coefficient.

4. **Option 4: $ Vm^{2}A^{-2}wb $**

This option suggests a unit of $ V \cdot m^2 \cdot A^{-2} \cdot wb $. The presence of $ wb $ instead of $ wb^{-1} $ and the incorrect power of $ A $ makes this option incorrect, as it does not match the derived unit for the Hall Coefficient.

In conclusion, Option 1 is the correct unit for the Hall Coefficient, as it accurately reflects the relationship between the electric field, current density, and magnetic field in the context of the Hall effect.