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. \(E=\dfrac{J}{\sigma}\)
3 and 1
3 and 1 — option (D), as recorded in the supplied key.
The point the item is really testing, and it is worth stating before anything else: none of the four expressions is a Maxwell equation. Maxwell’s four equations are these :
| Law | Differential form |
|---|---|
| Gauss’s law for electricity | \(\nabla\cdot\vec{D}=\rho\) |
| Gauss’s law for magnetism | \(\nabla\cdot\vec{B}=0\) |
| Faraday’s law | \(\nabla\times\vec{E}=-\dfrac{\partial\vec{B}}{\partial t}\) |
| Ampere’s law with Maxwell’s correction | \(\nabla\times\vec{H}=\vec{J}+\dfrac{\partial\vec{D}}{\partial t}\) |
Every one contains a divergence or a curl. The expressions in the question contain neither.
What they are instead: constitutive relations. These are the auxiliary equations describing how a medium responds, and Maxwell’s equations cannot be solved without them because they are what ties \(\vec{D}\) to \(\vec{E}\), \(\vec{B}\) to \(\vec{H}\) and \(\vec{J}\) to \(\vec{E}\) :
| Item | Expression | Verdict |
|---|---|---|
| 1 | \(B=\mu H\) | A valid constitutive relation — the magnetic one |
| 3 | \(E=J/\sigma\) | A valid constitutive relation — the point form of Ohm’s law, \(J=\sigma E\) |
| 2 | \(E=D/\varepsilon\) | Also dimensionally sound — it is \(D=\varepsilon E\) rearranged |
| 4 | \(E=\varepsilon D\) | Wrong — the permittivity is on the wrong side. Dimensionally impossible, and the one item that can be rejected outright |
How to eliminate under time pressure. Item 4 is the giveaway: \(D=\varepsilon E\), so \(E=D/\varepsilon\), never \(E=\varepsilon D\). Any option containing 4 can be struck out, which disposes of (B) immediately.
Note on the recorded answer. The key records (D), items 3 and 1. Item 2 is the dielectric relation written in the same rearranged style as item 3 and is equally sound, so a candidate could reasonably argue for option (A). The answer stored here follows the supplied key; what matters for the syllabus is the distinction between Maxwell’s four field equations and the constitutive relations that accompany them.
Similar Questions
For a steady magnetic fields, which of the following is true :
1. The tangential component of magnetic field is continuous across any boundary except the surface of perfect conductor.
2. The tangential component of magnetic flux density is continuous across any boundary.
3. The normal component of magnetic flux density is continuous across any boundary.
4. The normal component of electric field is continuous across the boundary.Which one of the following is correct ?
An electromagnetic wave is propagating in free space. Identify the correct situation out of the following
The unit of \(\left(\sigma E + \frac{\partial D}{\partial t}\right)\) is
As per the Maxwell's equations and their applications {Let all symbols are used with their usual meaning}
A. The tangential component of electric flux density, at a conducting surface, is a non zero quantity.
B. Electric field intensity can be found as \(E = \nabla V\).
C. For a time varying field the value of \(\oint \vec{E}\cdot \vec{dl}\) will be non-zero
D. The value of current flowing in the wire will be equal to \(\oint \vec{H}\cdot \vec{dl}\)
E. The magneto static field is conservative in nature.
Choose the correct answer from the options given below :
Which one of the fundamental equation was modified by Maxwell to form the basis of electro magnetic theory?
A medium has the value of displacement flux density
\(\overline{D}=20xy^{2}(z+1)\hat{a}_{x}+20x^{2}y(z+1)\hat{a}_{y}+10x^{2}y^{2}\hat{a}_{z}\ \text{Coulomb/m}^{2}\)
The volume charge density at a point P(0.3, 0.4, 0.5) is given by :
Consider the following statements regarding Maxwell's equations in differential form (Symbols have their usual meanings) :
(a) For free space \(\nabla\times\overline{H}=(\sigma+j\omega\epsilon)\overline{E}\)
(b) For free space \(\nabla\cdot\overline{D}=\rho\)
(c) For steady current \(\nabla\times\overline{H}=\overline{J}\)
(d) For static electric field \(\nabla\cdot\overline{D}=\rho\)Of these statements :
Match the following :
List - I List - II (a) \(\nabla\cdot\overline{D}\) (i) 0 (b) \(\nabla\cdot\overline{B}\) (ii) \(\overline{J}+\dfrac{\partial\overline{D}}{\partial t}\) (c) \(\nabla\times\overline{H}\) (iii) \(-\dfrac{\partial\overline{B}}{\partial t}\) (d) \(\nabla\times\overline{E}\) (iv) \(\rho_{v}\) Codes :
Match List – I with List – II and select the correct answer using codes given below :
List – I List – II a. \(\nabla\times\overline{H}\) i. \(\rho_{v}\) b. \(\nabla\cdot\overline{D}\) ii. \(-\dfrac{\partial B}{\partial t}\) c. \(\nabla\times\overline{E}\) iii. \(\overline{J}+\dfrac{\partial\overline{D}}{\partial t}\) d. \(\nabla\cdot\left(\nabla\times\overline{B}\right)\) iv. 0 Codes :
If Es is the field intensity vector identified as a phasor by its subscript ‘S’ and ko is the wave number, equation \(\nabla^{2}\mathbf{E}_S=-k^{2}\mathbf{E}_S\) is known as :
Important Questions from Maxwell's Equations
∇ × H = J is differential form of
"Time-varying magnetic field will always produce an electric field".
The given statement is true for:
Which of the following equations is based on Ampere's circuit law?
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?
Which of the following laws do not form a Maxwell’s equation?
