Question

Write Maxwell’s equation and give its physical significance.

Answer 1

The Maxwell’s equation and their physical significances are :

1. Maxwell’s first equation is ∇. D = ρ

Integrating this over an arbitrary volume V we get

∫v ∇.D dV = ∫v ρ dV.

But from Gauss Theorem, we get

∫s D.dS = ∫v ρ dV = q

Here, q is the net charge contained in volume V. S is the surface bounding volume V. Therefore,

Maxwell’s first equation signifies that:

The total electric displacement through the surface enclosing a volume is equal to the total charge within the volume.

2. Maxwell’s second equations is ∇.B = 0

Integrating this over an arbitrary volume V, we get

∫v ∇.B = 0.

Using Gauss divergence theorem to change volume integral into surface integral, we get

∫s B.dS = 0.

Maxwell’s second equation signifies that:
The total outward flux of magnetic induction B through any closed surface S is equal to zero.

3. Maxwell’s third equation is ∇ x E = `((- ∂B)/(∂t))` . dS

Converting the surface integral of left hand side into line integral by Stoke’s theorem, we get

`Φc E. dI = - (∫s ∂B)/(∂t). dS.`

Maxwell’s third equation signifies that:

The electromotive force (e.m.f. e = ∫C E.dI) around a closed path is equal to negative rate of change of magnetic flux linked with the path (since magnetic flux Φ = ∫s B.dS).

4. Maxwell’s fourth equation is

`∇ x H = J + (∂D)/(∂t)`

Taking surface integral over surface S bounded by curve C, we obtain

∫s ∇ x H. dS = ∫s (J + ∂D/∂t) dS

Using Stoke’s theorem to convert surface integral on L.H.S. of above equation into line integral, we get

`Φc H.dI = ∫s (J + (∂D)/(∂t)).dS`

Maxwell’s fourth equation signifies that:
The magneto motive force (m.m.f. = Φc H. dI) around a closed path is equal to the conduction current plus displacement current through any surface bounded by the path.