Question

Show that N/C and V/m are the units of the same physical quantity. Name that physical quantity.

Hint:

Electric field intensity can be expressed in both N/C and V/m, as they represent the same physical quantity.

Answer 1

Step 1: Understanding the Units of N/C.
The unit N/C is the unit of electric field intensity. In terms of base units: \[ \text{N} = \frac{\text{kg} \cdot \text{m}}{\text{s}^2}, \quad \text{C} = \text{coulomb} \] Thus, the unit N/C is: \[ \frac{\text{kg} \cdot \text{m}}{\text{s}^2 \cdot \text{C}} \]
Step 2: Understanding the Units of V/m.
The unit V/m is also the unit of electric field intensity. Voltage (V) is defined as: \[ \text{V} = \frac{\text{J}}{\text{C}} = \frac{\text{kg} \cdot \text{m}^2}{\text{s}^3 \cdot \text{C}} \] Thus, the unit V/m is: \[ \frac{\text{kg} \cdot \text{m}^2}{\text{s}^3 \cdot \text{C} \cdot \text{m}} = \frac{\text{kg} \cdot \text{m}}{\text{s}^3 \cdot \text{C}} \]
Step 3: Comparison.
From both calculations, we can see that the units of N/C and V/m are the same. Hence, both N/C and V/m are the units of electric field intensity.
Final Answer:
Both N/C and V/m are the units of electric field intensity.