1 `Vm^(-1)` equals

Options

A. 1N
B. `1Nm^(-1)`
C. `1 Nc^(-1)`
D. `1JC`

Explanation

To solve the question "1 Vm^(-1) equals," we need to understand the units involved and their relationships.

### Step-by-Step Solution:

1. **Understanding the Unit**:
- The unit "Vm^(-1)" stands for "volt per meter." This is a unit of electric field strength.

2. **Definition of Electric Field**:
- The electric field (E) is defined as the force (F) experienced by a unit charge (Q) placed in the field. Mathematically, this is expressed as:
\[ E = \frac{F}{Q} \]

3. **Relating Electric Field to Voltage**:
- The electric field can also be defined in terms of electric potential (V) and distance (d):
\[ E = -\frac{dV}{dx} \]
- In a uniform electric field, this simplifies to:
\[ E = \frac{V}{d} \]
- Where V is the voltage and d is the distance over which the potential changes.

4. **Unit Conversion**:
- From the definition of electric field, we can express it in terms of force and charge:
\[ E = \frac{F}{Q} \]
- The SI unit of force (F) is Newton (N), and the SI unit of charge (Q) is Coulomb (C).
- Therefore, the unit of electric field can also be expressed as:
\[ E = \frac{\text{Newton}}{\text{Coulomb}} = \text{N/C} \]

5. **Equating Units**:
- Now, we can equate the units:
\[ 1 \text{ Vm}^{-1} = 1 \text{ N/C} \]
- This means that 1 volt per meter is equivalent to 1 Newton per Coulomb.

6. **Final Expression**:
- Thus, we can conclude:
\[ 1 \text{ Vm}^{-1} = 1 \text{ N/C} = 1 \text{ Newton per Coulomb} \]

### Final Answer:
1 Vm^(-1) equals 1 Newton per Coulomb (1 N/C).