$${1 \frac{\text{V}}{\text{m}} = \frac{1 \text{J}}{1 \text{C} \cdot 1 \text{m}} = \frac{1 \text{N} \cdot 1 \text{m}}{1 \text{C} \cdot 1 \text{m}} = 1 \frac{\text{N}}{\text{C}}}$$