Consider the following statements regarding Maxwell's equations : 1. The total electric flux density or total electric displacement through the surface enclosing a volume $v$ is equal to the total charge within the volume. 2. Net electric flux emerging through any closed surface is zero. 3. The magnetomotive force around a closed path is equal to the time derivative of the magnetic flux density or magnetic displacement through any surface bounded by the surface. Which of the above statements are not correct?
Maxwell's Equations Statement Analysis
This solution evaluates the correctness of statements regarding Maxwell's equations and identifies the incorrect ones.
Statement 1: Gauss's Law for Electricity
This statement accurately describes Gauss's Law for electricity. It states that the total electric displacement ($ \vec{D} $) through a closed surface equals the total charge enclosed ($ Q_{enc} $) within that surface. Mathematically, this is represented as:
$ \oint_S \vec{D} \cdot d\vec{A} = Q_{enc} $
Thus, statement 1 is correct.
Statement 2: Net Electric Flux
The statement claims that the net electric flux emerging through any closed surface is zero. This contradicts Gauss's Law for electricity ($ \oint_S \vec{E} \cdot d\vec{A} = \frac{Q_{enc}}{\epsilon_0} $). The net flux is proportional to the enclosed charge ($ Q_{enc} $). It is zero only if there is no net charge inside the surface. As a general principle, this statement is incorrect.
Statement 3: Magnetomotive Force and Magnetic Flux
This statement relates magnetomotive force (related to the line integral of the magnetic field intensity, $ \vec{H} $) to the time derivative of magnetic flux density ($ \vec{B} $). This is not a correct formulation of any of Maxwell's equations. Faraday's Law relates electromotive force (related to $ \vec{E} $) to the time rate of change of magnetic flux ($ \Phi_B = \int \vec{B} \cdot d\vec{A} $):
$ \oint_S \vec{E} \cdot d\vec{l} = -\frac{\partial \Phi_B}{\partial t} $
Ampere's Law (with Maxwell's addition) relates the line integral of $ \vec{H} $ to electric current and the time rate of change of electric displacement ($ \vec{D} $). The statement provided is fundamentally flawed and thus incorrect.
Conclusion: Incorrect Maxwell's Equations Statements
Based on the analysis:
- Statement 1 is correct.
- Statement 2 is incorrect.
- Statement 3 is incorrect.
Therefore, the statements that are not correct are 2 and 3.
This corresponds to Option C.
Important Questions from Maxwell's Equations
∇ × H = J is differential form of
Maxwell's divergence equation for the magnetic field is given by _______.
If flux density is represented by 'B' and magnetic field is represented by 'H' in a magnetic circuit, then what will be the energy density in the magnetic field?
Maxwell's third equation is derived from _______.
Which law is represented by the given expression?
\(\int B.dl = \mu_oi_c+\mu_0\epsilon_0 \frac{d \Phi_E}{dt}\)
