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Which among the following does not repre...

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

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)`

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The correct Answer is:
To determine which option does not represent Maxwell's equations, we first need to understand the four fundamental equations that comprise Maxwell's equations. They are: 1. **Gauss's Law for Electricity**: \[ \oint \mathbf{E} \cdot d\mathbf{A} = \frac{Q_{enc}}{\varepsilon_0} \] This relates the electric field \(\mathbf{E}\) to the charge \(Q_{enc}\) enclosed in a surface. 2. **Gauss's Law for Magnetism**: \[ \oint \mathbf{B} \cdot d\mathbf{A} = 0 \] This states that there are no magnetic monopoles; the net magnetic flux through a closed surface is zero. 3. **Faraday's Law of Induction**: \[ \oint \mathbf{E} \cdot d\mathbf{l} = -\frac{d\Phi_B}{dt} \] This indicates that a changing magnetic field \(\Phi_B\) induces an electric field \(\mathbf{E}\). 4. **Ampère-Maxwell Law**: \[ \oint \mathbf{B} \cdot d\mathbf{l} = \mu_0 I_{enc} + \mu_0 \varepsilon_0 \frac{d\Phi_E}{dt} \] This law relates the magnetic field \(\mathbf{B}\) to the electric current \(I_{enc}\) and the changing electric field \(\Phi_E\). Now, let's analyze the options provided in the question: 1. **Option 1**: Represents Gauss's Law for Electricity. 2. **Option 2**: Represents Gauss's Law for Magnetism. 3. **Option 3**: Represents Faraday's Law of Induction, but it is incorrectly stated as \(E \cdot dL = -D\Phi_I/Dt\) instead of the correct form. 4. **Option 4**: Represents the displacement current term in the Ampère-Maxwell Law. From the analysis, it is clear that **Option 3** does not correctly represent Maxwell's equations because it misstates Faraday's Law. ### Final Answer: **Option 3 does not represent Maxwell's equation correctly.**

To determine which option does not represent Maxwell's equations, we first need to understand the four fundamental equations that comprise Maxwell's equations. They are: 1. **Gauss's Law for Electricity**: \[ \oint \mathbf{E} \cdot d\mathbf{A} = \frac{Q_{enc}}{\varepsilon_0} \] This relates the electric field \(\mathbf{E}\) to the charge \(Q_{enc}\) enclosed in a surface. ...
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