Correct Answer - Option 3 :
∇ × H = B + J
Explanation:
The correct Maxwell's equation is:
\(\nabla \times H =J_C \ + \ J_ D\)
\(\nabla \times H =J+ \frac{{\partial D}}{{\partial t}}\)
This law is known as Ampere's circuital law in differential form.
Hence the solution is option (3).
Maxwell's Equations for time-varying fields is as shown:
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S. No.
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Differential form
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Integral form
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Name
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1.
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\(\nabla \times E = - \frac{{\partial B}}{{\partial t}}\)
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\(\mathop \oint \nolimits_L^{} E.dl = - \frac{\partial }{{\partial t}}\mathop \smallint \nolimits_S^{} B.d S\)
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Faraday’s law of electromagnetic induction
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2.
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\(\nabla \times H =J+ \frac{{\partial D}}{{\partial t}}\)
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\(\mathop \oint \nolimits_L^{} H.dl = \mathop \smallint \nolimits_S^{} (J+\frac{{\partial D}}{{\partial t}}).dS\)
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Ampere’s circuital law
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3.
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∇ . D = ρv
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\(\mathop \oint \nolimits_S^{} D.dS = \mathop \smallint \nolimits_v^{} \rho_v.dV\)
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Gauss’ law
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4.
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∇ . B = 0
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\(\mathop \oint \nolimits_S^{} B.dS = 0\)
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Gauss’ law of Magnetostatics (non-existence of magnetic monopole)
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