The ratio of electric force between two electrons to two protons separated by the same distance in air is

Options

A. `10^0`
B. `10^6`
C. `10^4`
D. None of the above

Explanation

To find the ratio of the electric force between two electrons to the electric force between two protons, we can use Coulomb's law, which states that the electric force \( F \) between two point charges is given by the formula:

\[ F = \frac{k \cdot q_1 \cdot q_2}{r^2} \]

where:
- \( k \) is Coulomb's constant,
- \( q_1 \) and \( q_2 \) are the magnitudes of the charges,
- \( r \) is the distance between the charges.

### Step 1: Calculate the force between two electrons
Let the charge of an electron be \( e = 1.6 \times 10^{-19} \) coulombs. The force \( F_1 \) between two electrons can be expressed as:

\[ F_1 = \frac{k \cdot e \cdot e}{r^2} = \frac{k \cdot e^2}{r^2} \]

### Step 2: Calculate the force between two protons
The charge of a proton is also \( e = 1.6 \times 10^{-19} \) coulombs (but positive). The force \( F_2 \) between two protons can be expressed as:

\[ F_2 = \frac{k \cdot e \cdot e}{r^2} = \frac{k \cdot e^2}{r^2} \]

### Step 3: Find the ratio of the forces
Now, we need to find the ratio of the electric force between the two electrons to the electric force between the two protons:

\[ \text{Ratio} = \frac{F_1}{F_2} = \frac{\frac{k \cdot e^2}{r^2}}{\frac{k \cdot e^2}{r^2}} = \frac{k \cdot e^2}{r^2} \div \frac{k \cdot e^2}{r^2} \]

### Step 4: Simplify the ratio
Since both forces \( F_1 \) and \( F_2 \) are equal, we can simplify the ratio:

\[ \text{Ratio} = 1 \]

### Conclusion
The ratio of the electric force between two electrons to the electric force between two protons, separated by the same distance in air, is \( 1 \) or \( 10^0 \).

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