1. Concept: The standard unit of Electric Field Intensity can be mathematically proven via two separate defining equations (Force vs Gradient) to be entirely interchangeable.
2. Formula: $$ E = \frac{F}{q} \implies \text{N/C} \quad \text{and} \quad E = \frac{V}{d} \implies \text{V/m} $$
3. Solution: - Start with Volts per meter (V/m).
- Expand Volt into Joules per Coulomb (J/C): \( \frac{\text{J/C}}{\text{m}} = \frac{\text{J}}{\text{C} \cdot \text{m}} \).
- Expand Joule into Newton-meters (N·m): \( \frac{\text{N} \cdot \text{m}}{\text{C} \cdot \text{m}} \).
- The meters mutually cancel, resulting perfectly in Newtons per Coulomb (N/C).
4. Why other options are incorrect: 1 J/C defines 1 Volt, not an electric field. 1 J/sec defines 1 Watt of Power. 1 C/m³ represents volumetric charge density.
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