Which one of the fundamental equation was modified by Maxwell to form the basis of electro magnetic theory?
Ampere Law
The law Maxwell amended. Ampère's circuital law originally read
\(\nabla\times\vec{H}=\vec{J}\)
i.e. only a conduction current can curl the magnetic field. Maxwell added the displacement current term:
\(\nabla\times\vec{H}=\vec{J}+\dfrac{\partial \vec{D}}{\partial t}\)
Why the fix was necessary. Take the divergence of the original form. Since \(\nabla\cdot(\nabla\times\vec{H})=0\) identically, it demands \(\nabla\cdot\vec{J}=0\) — but the continuity equation says
\(\nabla\cdot\vec{J}=-\dfrac{\partial\rho_v}{\partial t}\)
which is non-zero wherever charge accumulates. The classic illustration is a capacitor being charged: conduction current flows in the leads but stops at the plates, so a loop drawn between the plates would enclose no current, yet a magnetic field is certainly present. The displacement current \(\partial\vec{D}/\partial t\) flowing through the gap restores continuity.
Why it created electromagnetic theory. With the new term, a changing electric field produces a magnetic field just as Faraday's law has a changing magnetic field produce an electric field. The two effects feed each other, and combining the curl equations gives the wave equation with velocity
\(c=\dfrac{1}{\sqrt{\mu_0\varepsilon_0}}\approx 3\times10^{8}\ \text{m/s}\)
— matching the measured speed of light and identifying light itself as an electromagnetic wave.
Why the other three needed no change. Gauss's law of electrostatics \(\nabla\cdot\vec{D}=\rho_v\) and Gauss's law for magnetism \(\nabla\cdot\vec{B}=0\) already hold for time-varying fields as written, and Faraday's law \(\nabla\times\vec{E}=-\partial\vec{B}/\partial t\) was formulated for time-varying fields from the start.
Hence, the equation Maxwell modified is Ampère's law.
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 ?
Which of the following are Maxwell equations ?
1. \(B=\mu H\)
2. \(E=\dfrac{D}{\epsilon}\)
3. \(E=\dfrac{J}{\sigma}\)4. \(E=\epsilon D\)
Select the correct answer :
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 :
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?
