Question

One of the following is not Maxwell’s equation

1. ∇ ⋅ D = Pv
2.  ∇ ⋅ B = J
3. \(\nabla \times \bar E =- \frac{{\partial \bar B}}{{\partial t}}\)
4. \(\nabla \times \bar H = \frac{{\partial \bar D}}{{\partial t}} + \bar J\)

Answer 1

Correct Answer - Option 2 :  ∇ ⋅ B = J

Concept:

The correct Maxwell's equation is:

∇ . B = 0

 

Maxwell's Equations for time-varying fields is as shown:

S. No.	Differential form	Integral form	Name
1.	\(\nabla \times E = - \frac{{\partial B}}{{\partial t}}\)	\(\mathop \oint \nolimits_L^{} E.dl = - \frac{\partial }{{\partial t}}\mathop \smallint \nolimits_S^{} B.d S\)	Faraday’s law of electromagnetic induction
2.	\(\nabla \times H =J+ \frac{{\partial D}}{{\partial t}}\)	\(\mathop \oint \nolimits_L^{} H.dl = \mathop \smallint \nolimits_S^{} (J+\frac{{\partial D}}{{\partial t}}).dS\)	Ampere’s circuital law
3.	∇ . D = ρv	\(\mathop \oint \nolimits_S^{} D.dS = \mathop \smallint \nolimits_v^{} \rho_v.dV\)	Gauss’ law
4.	∇ . B = 0	\(\mathop \oint \nolimits_S^{} B.dS = 0\)	Gauss’ law of Magnetostatics (non-existence of magnetic monopole)