The unit of \(\left(\sigma E + \frac{\partial D}{\partial t}\right)\) is
Ampere / meter2
Where the expression comes from. It is the right-hand side of Maxwell's curl-H equation (Ampère's law with Maxwell's correction):
\(\nabla\times H = \sigma E + \dfrac{\partial D}{\partial t} = J_c + J_d\)
Term 1 — conduction current density. \(J_c=\sigma E\) is the point form of Ohm's law. Checking the units: conductivity σ is in siemens per metre (S/m) and the electric field E is in volts per metre (V/m), so
\(\left[\sigma E\right]=\dfrac{S}{m}\times\dfrac{V}{m}=\dfrac{A}{m^{2}}\)
(using S·V = A).
Term 2 — displacement current density. The electric flux density D is in coulombs per square metre (C/m²), and differentiating with respect to time divides by seconds:
\(\left[\dfrac{\partial D}{\partial t}\right]=\dfrac{C/m^{2}}{s}=\dfrac{C/s}{m^{2}}=\dfrac{A}{m^{2}}\)
Add them. Only quantities of like units may be added, and both terms are current densities, so the sum is a current density in A/m².
Cross-check with the left-hand side. The magnetic field intensity H is in A/m, and the curl operator introduces a spatial derivative, i.e. an extra 1/m:
\(\left[\nabla\times H\right]=\dfrac{A/m}{m}=\dfrac{A}{m^{2}}\) ✓
Both sides agree, as they must.
Physical significance. The conduction term dominates in a good conductor and the displacement term in a good dielectric; their ratio \(\sigma/\omega\varepsilon\) is the loss tangent, which decides whether a medium behaves as a conductor or an insulator at a given frequency. Maxwell's addition of \(\partial D/\partial t\) is what makes current continuous through a capacitor and what allows electromagnetic waves to exist in free space at all.
Ruling out the others. A/m is the unit of H (or of magnetisation), while A·m² is the unit of magnetic dipole moment and A·m of current moment — none of them is a density per unit area.
Hence, the unit of the expression is ampere/metre².
Similar Questions
An electromagnetic wave is propagating in free space. Identify the correct situation out of the following
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?
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 :
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 :
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(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 :
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 :
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?
\(\int B.dl = \mu_oi_c+\mu_0\epsilon_0 \frac{d \Phi_E}{dt}\)
