Gauss’s law should be invalid if

Options

A. There were magnetic monopoles
B. The inverse square law were not exactly true
C. The velocity of light were not a universal constant
D. None of these

Answer

To determine under what conditions Gauss's law would be invalid, we need to analyze the given options carefully. Gauss's law states that the electric flux through a closed surface is proportional to the charge enclosed within that surface. Mathematically, it is expressed as:

\[ \Phi_E = \oint \mathbf{E} \cdot d\mathbf{S} = \frac{Q_{\text{enc}}}{\epsilon_0} \]

Where:
- \(\Phi_E\) is the electric flux,
- \(\mathbf{E}\) is the electric field,
- \(d\mathbf{S}\) is the differential area vector,
- \(Q_{\text{enc}}\) is the enclosed charge,
- \(\epsilon_0\) is the permittivity of free space.

Now, let's evaluate each option:

1. **If there were magnetic monopoles**:
- Magnetic monopoles would imply the existence of isolated north or south magnetic poles. However, Gauss's law is specifically formulated for electric fields and charges, not magnetic fields. Hence, the existence of magnetic monopoles does not invalidate Gauss's law for electric fields.

2. **If the inverse square law is not exactly true**:
- The inverse square law states that the electric field due to a point charge decreases with the square of the distance from the charge. Gauss's law is derived based on this principle. If the inverse square law were not true, then the relationship between electric field and charge would not hold, thus invalidating Gauss's law.

3. **If the velocity of light were not a universal constant**:
- The velocity of light being a universal constant is related to electromagnetic theory and the propagation of electromagnetic waves. However, Gauss's law itself does not depend on the speed of light. Therefore, this condition does not invalidate Gauss's law.

4. **None of these**:
- This option suggests that none of the previous conditions would invalidate Gauss's law. However, we have already established that the second option does.

Based on this analysis, the correct answer is that Gauss's law would be invalid if the inverse square law is not exactly true.

### Final Answer:
Gauss's law should be invalid if the inverse square law is not exactly true.