In Coulomb's law, the constant of proportionality K has the units

Options

A. `N `
B. `Nm ^(2)`
C. `NC ^(2) //m^(2)`
D. `Nm ^(2) //C ^(2)`

Explanation

To determine the units of the constant of proportionality \( K \) in Coulomb's law, we start with the formula given by Coulomb's law:

\[ F = K \frac{Q_1 Q_2}{r^2} \]

Where:
- \( F \) is the force between the charges,
- \( Q_1 \) and \( Q_2 \) are the magnitudes of the charges,
- \( r \) is the distance between the charges,
- \( K \) is the constant of proportionality.

### Step 1: Rearranging the formula
We can rearrange the formula to solve for \( K \):

\[ K = \frac{F \cdot r^2}{Q_1 Q_2} \]

### Step 2: Identifying the units
Next, we need to identify the units of each component in the formula:

- The SI unit of force \( F \) is Newton (N).
- The SI unit of distance \( r \) is meter (m), so \( r^2 \) will have the unit \( m^2 \).
- The SI unit of charge \( Q_1 \) and \( Q_2 \) is Coulomb (C).

### Step 3: Substituting the units
Now, we can substitute the units into the equation for \( K \):

\[ K = \frac{\text{N} \cdot \text{m}^2}{\text{C} \cdot \text{C}} = \frac{\text{N} \cdot \text{m}^2}{\text{C}^2} \]

### Step 4: Final expression
Thus, the unit of the constant \( K \) in Coulomb's law is:

\[ K = \frac{\text{N} \cdot \text{m}^2}{\text{C}^2} \]

### Conclusion
Therefore, the units of the constant of proportionality \( K \) in Coulomb's law are \( \text{N} \cdot \text{m}^2/\text{C}^2 \).

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