Which of the following are Maxwell equations ? 1. \(B=\mu H\) 2. \(E=\dfrac{D}{\epsilon}\) 4. \(E=\epsilon D\) Select the correct answer :
3. \(E=\dfrac{J}{\sigma}\)
1, 2 and 3
Relation 4 is dimensionally wrong, and the other three are correct — so the answer is 1, 2 and 3, option 1.
Testing relation 4. The defining relation between the electric field and the flux density is
\(D=\varepsilon E\quad\Rightarrow\quad E=\dfrac{D}{\varepsilon}\)
which is exactly what relation 2 states. Relation 4 writes \(E=\varepsilon D\), multiplying where it should divide — the same equation with the permittivity on the wrong side. Since \(\varepsilon\) is not dimensionless, only one of the two can be right, and relation 2 is it. That single check eliminates options 2, and options 3 and 4 fall because each omits one of the three valid relations.
| Relation | Name | Verdict |
|---|---|---|
| 1. B = μH | Magnetic constitutive relation | ✓ |
| 2. E = D/ε | Electric constitutive relation | ✓ |
| 3. E = J/σ | Ohm's law in point form | ✓ |
| 4. E = εD | — | ✗ Inverted |
A point about the terminology, which is why the answer is flagged. Strictly, none of the four is a Maxwell equation. Maxwell's four are
\(\nabla\cdot\vec{D}=\rho,\qquad \nabla\cdot\vec{B}=0\)
\(\nabla\times\vec{E}=-\dfrac{\partial\vec{B}}{\partial t},\qquad \nabla\times\vec{H}=\vec{J}+\dfrac{\partial\vec{D}}{\partial t}\)
The relations listed in the question are the constitutive relations — sometimes called the auxiliary or subsidiary equations — which describe how a material responds, through \(\mu\), \(\varepsilon\) and \(\sigma\). Many textbooks list them alongside Maxwell's equations as a set of seven, since they are indispensable: Maxwell's four relate \(\vec{E},\vec{D},\vec{B},\vec{H}\) and \(\vec{J}\), but without the constitutive relations there are more unknowns than equations and no problem can be solved. It is in that sense that the question means "Maxwell equations", and on that reading the three valid ones are the answer.
Hence, the correct set is 1, 2 and 3.
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4. The normal component of electric field is continuous across the boundary.Which one of the following is correct ?
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Which law is represented by the given expression?
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