`1 Vm ^(-1) ` equals

Options

A. `1 NC ^(-1)`
B. `1 NC ^(-2)`
C. `1 Jm ^(-1)`
D. `1 Jm ^(-2)`

Explanation

To solve the question "1 Vm^(-1) equals", we will break it down step by step.

### Step-by-Step Solution:

1. **Understanding the Units**:
We start with the unit "1 volt per meter" which can also be expressed as "1 volt meter^(-1)".

**Hint**: Remember that "per meter" can be written as "meter^(-1)".

2. **Relating Voltage to Work and Charge**:
The voltage (V) is defined as the work done (W) per unit charge (Q). The formula is:
\[ V = \frac{W}{Q} \]
where:
- \( V \) is in volts,
- \( W \) is in joules,
- \( Q \) is in coulombs.

**Hint**: Voltage is a measure of potential difference and is related to work done and charge.

3. **Expressing Work Done**:
Work done (W) can be expressed as:
\[ W = \text{Force} \times \text{Displacement} \]
The unit of work is joules (J), where:
- Force is measured in newtons (N),
- Displacement is measured in meters (m).

**Hint**: Joules can be broken down into newton-meters.

4. **Substituting Work Done into Voltage**:
Substituting the expression for work into the voltage formula gives:
\[ V = \frac{F \times d}{Q} \]
where \( F \) is force and \( d \) is displacement.

**Hint**: Keep in mind that force and displacement are related to work.

5. **Rearranging the Units**:
Now, substituting the units into the equation:
\[ 1 \, \text{volt} = \frac{1 \, \text{newton} \times 1 \, \text{meter}}{1 \, \text{coulomb}} \]
This means:
\[ 1 \, \text{volt} = 1 \, \text{newton meter} \, \text{coulomb}^{-1} \]

**Hint**: Make sure to keep track of the units as you substitute them.

6. **Final Expression**:
Therefore, when we express "1 volt per meter" (or "1 volt meter^(-1)"):
\[ 1 \, \text{volt meter}^{-1} = 1 \, \text{newton coulomb}^{-1} \]

**Hint**: You can cancel out the meter units to simplify the expression.

### Conclusion:
Thus, we conclude that:
\[ 1 \, \text{Vm}^{-1} = 1 \, \text{N C}^{-1} \]

### Final Answer:
1 Vm^(-1) equals 1 N C^(-1).