Let E,G and N represent the magnitudes of electromagnetic, gravitational and nuclear forces between two electrons at a given separation. Then

Options

A. `NgtEgtG`
B. `EgtNgtG`
C. `GgtNgtE`
D. `EgtGgtN`

Answer

To solve the problem, we need to compare the magnitudes of the electromagnetic force (E), gravitational force (G), and nuclear force (N) between two electrons at a given separation.

### Step-by-Step Solution:

1. **Understanding the Forces**:
- The three forces we are comparing are:
- **Electromagnetic Force (E)**: The force between two charged particles.
- **Gravitational Force (G)**: The force between two masses.
- **Nuclear Force (N)**: The force that acts between nucleons (protons and neutrons) in an atomic nucleus.

2. **Nuclear Force (N)**:
- The nuclear force is a short-range force that is significant only at distances smaller than about \(10^{-12}\) meters (Fermi scale).
- Since the problem does not specify the separation distance and we can assume it is greater than the Fermi scale, we conclude that the nuclear force (N) is negligible compared to the other two forces.

**Conclusion**: \(N\) is the smallest force.

3. **Electromagnetic Force (E)**:
- The formula for the electromagnetic force between two charged particles is given by:
\[ E = k \frac{q_1 q_2}{d^2} \]
where \(k\) is Coulomb's constant (\(9 \times 10^9 \, \text{N m}^2/\text{C}^2\)), \(q_1\) and \(q_2\) are the charges of the electrons (\(1.6 \times 10^{-19} \, \text{C}\)), and \(d\) is the separation distance.

4. **Gravitational Force (G)**:
- The formula for the gravitational force between two masses is given by:
\[ G = G \frac{m_1 m_2}{d^2} \]
where \(G\) is the gravitational constant (\(6.67 \times 10^{-11} \, \text{N m}^2/\text{kg}^2\)), and \(m_1\) and \(m_2\) are the masses of the electrons (\(9.11 \times 10^{-31} \, \text{kg}\)).

5. **Calculating the Forces**:
- Assume a separation distance \(d = 1 \, \text{m}\):
- **Electromagnetic Force (E)**:
\[ E = 9 \times 10^9 \frac{(1.6 \times 10^{-19})^2}{1^2} = 9 \times 10^9 \times 2.56 \times 10^{-38} = 2.3 \times 10^{-28} \, \text{N} \]

- **Gravitational Force (G)**:
\[ G = 6.67 \times 10^{-11} \frac{(9.11 \times 10^{-31})^2}{1^2} = 6.67 \times 10^{-11} \times 8.27 \times 10^{-62} = 5.5 \times 10^{-71} \, \text{N} \]

6. **Comparing the Forces**:
- From the calculations:
- \(E = 2.3 \times 10^{-28} \, \text{N}\)
- \(G = 5.5 \times 10^{-71} \, \text{N}\)
- \(N\) is negligible.

- Since \(E\) is much larger than \(G\) and \(N\) is the smallest, we conclude:
\[ E > G > N \]

7. **Final Conclusion**:
- The correct order of the forces is:
\[ E > G > N \]