Maxwell's euqations describe the fundamental laws opf

Options

A. Only electricity
B. Only magnetism
C. Only machanics
D. Both (a) and (b)

Explanation

**Step-by-Step Solution:**

1. **Understanding Maxwell's Equations:**
Maxwell's equations are a set of four fundamental equations that describe how electric and magnetic fields interact and propagate. They form the foundation of classical electromagnetism, optics, and electric circuits.

2. **First Equation (Gauss's Law for Electricity):**
The first equation states that the surface integral of the electric field \( \mathbf{E} \) over a closed surface is equal to the charge enclosed \( Q_{\text{enc}} \) divided by the permittivity of free space \( \epsilon_0 \):
\[ \oint \mathbf{E} \cdot d\mathbf{A} = \frac{Q_{\text{enc}}}{\epsilon_0} \]
This law indicates that electric charges produce electric fields.

3. **Second Equation (Gauss's Law for Magnetism):**
The second equation states that the magnetic flux through a closed surface is always zero:
\[ \oint \mathbf{B} \cdot d\mathbf{A} = 0 \]
This implies that there are no magnetic monopoles; magnetic field lines are closed loops.

4. **Third Equation (Ampère-Maxwell Law):**
The third equation relates the line integral of the magnetic field \( \mathbf{B} \) around a closed loop to the total current \( I_{\text{enc}} \) passing through the loop and the displacement current \( \epsilon_0 \frac{d\Phi_E}{dt} \):
\[ \oint \mathbf{B} \cdot d\mathbf{l} = \mu_0 I_{\text{enc}} + \mu_0 \epsilon_0 \frac{d\Phi_E}{dt} \]
This shows that a changing electric field can produce a magnetic field.

5. **Fourth Equation (Faraday's Law of Induction):**
The fourth equation states that the line integral of the electric field \( \mathbf{E} \) around a closed loop is equal to the negative rate of change of the magnetic flux through the loop:
\[ \oint \mathbf{E} \cdot d\mathbf{l} = -\frac{d\Phi_B}{dt} \]
This indicates that a changing magnetic field can induce an electric field.

6. **Conclusion:**
Together, these four equations describe the fundamental laws of electricity and magnetism, showing how electric fields and magnetic fields are interconnected. Therefore, the answer to the question is that Maxwell's equations describe the fundamental laws of both electric and magnetic fields.

**Final Answer:**
Maxwell's equations describe the fundamental laws of both electricity and magnetism.

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