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$(A)$ time-varying magnetic field is generated by a time-varying electric current.$1$. A permanent magnet produces a static magnetic field.$2$. An ele

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$(D)$ only

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$(A)$ time-varying magnetic field is generated by a time-varying electric current.$1$. A permanent magnet produces a static magnetic field.$2$. An electric field changing linearly with time produces a constant displacement current $(I_d = \epsilon_0 \frac{d\Phi_E}{dt})$, which results in a constant magnetic field, not a time-varying one.$3$. Direct current produces a constant magnetic field.$4$. A decelerating charged particle is an accelerated charge, which produces time-varying electric and magnetic fields (electromagnetic waves).$5$. An antenna fed with a digital signal involves rapidly changing currents, which produce time-varying magnetic fields.Therefore, both $(D)$ and $(E)$ are sources of time-varying magnetic fields. However, based on the provided options, the most appropriate choice is $(D)$ and $(E)$ (Note: If the provided options are restricted, $(D)$ is the primary physical source mentioned).

List-$I$ (Relation)	List-$II$ (Law)
$A$. $\oint \overrightarrow{E} \cdot d\vec{l} = -\frac{d}{dt} \oint \overrightarrow{B} \cdot d\vec{a}$	$I$. Ampere's circuital law
$B$. $\oint \vec{B} \cdot d\vec{l} = \mu_0(I + \epsilon_0 \frac{d\phi_E}{dt})$	$II$. Faraday's laws of electromagnetic induction
$C$. $\oint \overrightarrow{E} \cdot d\vec{a} = \frac{1}{\epsilon_0} \int \rho dv$	$III$. Ampere-Maxwell law
$D$. $\oint \overrightarrow{B} \cdot d\vec{l} = \mu_0 I$	$IV$. Gauss's law of electrostatics

List-$I$	List-$II$
$(a)$ Gauss’ law for electrostatics	$(i)$ $\oint \vec{E} \cdot d\vec{A} = \frac{Q}{\epsilon_0}$
$(b)$ Gauss’ law for magnetism	(ii) $\oint \vec{B} \cdot d\vec{l} = \mu_0 [i_c + \epsilon_0 \frac{d\phi_E}{dt}]$
$(c)$ Faraday’s law	(iii) $\oint \vec{B} \cdot d\vec{A} = 0$
$(d)$ Ampere-Maxwell’s law	(iv) $\oint \vec{E} \cdot d\vec{l} = -\frac{d\phi_B}{dt}$

The source of a time-varying magnetic field may be:
$(A)$ A permanent magnet
$(B)$ An electric field changing linearly with time
$(C)$ Direct current
$(D)$ A decelerating charged particle
$(E)$ An antenna fed with a digital signal
Choose the correct answer from the options given below:

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The source of a time-varying magnetic field may be:$(A)$ A permanent magnet$(B)$ An electric field changing linearly with time$(C)$ Direct current$(D)$ A decelerating charged particle$(E)$ An antenna fed with a digital signalChoose the correct answer from the options given below: