The unit of electric field is not equivalent to

Options

A. N/C
B. J/C
C. V/m
D. J/C-m

Answer

To solve the problem of determining which unit of electric field is not equivalent, we need to analyze the units of electric field and the options provided.

### Step-by-Step Solution:

1. **Understanding the Electric Field**:
The electric field (E) is defined as the force (F) experienced per unit charge (q). Mathematically, this is expressed as:
\[ E = \frac{F}{q} \]

2. **Identifying the Units**:
- The unit of force (F) is Newton (N).
- The unit of charge (q) is Coulomb (C).
Therefore, the unit of electric field can be expressed as:
\[ E = \frac{\text{N}}{\text{C}} \]

3. **Converting Units**:
We can further analyze the unit of electric field by expressing Newton in terms of Joules and meters:
- 1 Joule (J) = 1 Newton (N) × 1 meter (m)
- Thus, we can rewrite Newton as:
\[ \text{N} = \frac{\text{J}}{\text{m}} \]
Substituting this into the electric field equation gives:
\[ E = \frac{\text{J/m}}{\text{C}} = \frac{\text{J}}{\text{C} \cdot \text{m}} \]

4. **Electric Field in Terms of Potential**:
The electric field can also be expressed in terms of electric potential (V) and distance (R):
\[ E = \frac{V}{R} \]
- The unit of electric potential (V) is Volt (V), and the unit of distance (R) is meter (m).
- Therefore, the unit of electric field in this context is:
\[ E = \frac{\text{V}}{\text{m}} \]

5. **Conclusion**:
After analyzing the units, we can conclude that the electric field can be expressed in several equivalent forms, but we need to identify which of the given options is not equivalent to these derived units.

### Final Answer:
The unit of electric field is not equivalent to the option that does not match the derived units of \(\frac{\text{N}}{\text{C}}\), \(\frac{\text{J}}{\text{C} \cdot \text{m}}\), or \(\frac{\text{V}}{\text{m}}\).