Which among the following does not represent Maxwell's equation?

Options

A. `ointvecE.vec(dA)=(q)/(epsilon_(0))`
B. `ointvecB.vec(dA)=0`
C. `ointvecE.vec(dl)=(-dB)/(dt)`
D. `oint vecB.vec(dl)=mu_(0)I_(C)+mu_(0)epsilon_(0)(dphi_(E))/(dt)`

Explanation

To determine which of the given equations does not represent Maxwell's equations, we will analyze each option based on Maxwell's four fundamental equations.

### Step-by-Step Solution:

1. **Identify the First Equation**:
- The first equation is given as:
\[ \oint \mathbf{E} \cdot d\mathbf{A} = \frac{Q}{\epsilon_0} \]
- This is **Gauss's Law for Electricity**, which states that the electric flux through a closed surface is proportional to the charge enclosed. This equation is correct.

2. **Identify the Second Equation**:
- The second equation is:
\[ \oint \mathbf{B} \cdot d\mathbf{A} = 0 \]
- This represents the absence of magnetic monopoles, indicating that the total magnetic flux through a closed surface is zero. This equation is also correct.

3. **Identify the Third Equation**:
- The third equation is:
\[ \oint \mathbf{E} \cdot d\mathbf{L} = -\frac{d\Phi_B}{dt} \]
- This is **Faraday's Law of Induction**, which states that the electromotive force (emf) around a closed loop is equal to the negative rate of change of magnetic flux through the loop. However, the equation provided in the question is incomplete as it does not include the area vector for the magnetic field. Therefore, this equation is not correctly representing Maxwell's equations.

4. **Identify the Fourth Equation**:
- The fourth equation is:
\[ \oint \mathbf{B} \cdot d\mathbf{L} = \mu_0 I + \mu_0 \epsilon_0 \frac{d\Phi_E}{dt} \]
- This is **Ampere-Maxwell Law**, which relates the magnetic field around a closed loop to the electric current and the rate of change of electric flux. This equation is correct.

5. **Conclusion**:
- Options 1, 2, and 4 are valid representations of Maxwell's equations, while option 3 is not correctly stated. Therefore, the answer is that the third equation does not represent Maxwell's equations.

### Final Answer:
The equation that does not represent Maxwell's equations is the third option.