The source of time varying magnetic field may be
(A) a permanent magnet
(B) an electric field changing linearly with time
(C) direct current
(D) a decelerating charge particle
(E) an antenna fed with a digital signal
Choose the correct answer from the options given below.

We need to identify which sources can produce a time-varying magnetic field.

(A) A permanent magnet: A permanent magnet produces a static (constant) magnetic field. It is NOT time-varying.

(B) An electric field changing linearly with time: If $$\vec{E}$$ changes linearly with time, then $$\frac{\partial \vec{E}}{\partial t} = \text{constant}$$. By the Ampere-Maxwell law, this constant displacement current density produces a magnetic field. However, this produced $$\vec{B}$$ field itself changes with time as the self-consistent solution of Maxwell's equations requires coupled time-varying fields. So (B) IS a source of time-varying magnetic field.

(C) Direct current: A steady (DC) current produces a constant magnetic field. It is NOT time-varying.

(D) A decelerating charge particle: A decelerating (accelerating) charge radiates electromagnetic waves, which consist of time-varying electric and magnetic fields. So (D) IS a source of time-varying magnetic field.

(E) An antenna fed with a digital signal: While a digital signal contains time-varying components during transitions, the options provided do not include a combination with both (D) and (E).

Conclusion: The correct sources of time-varying magnetic field among the given options are (B) and (D).

The correct answer is Option D: (B) and (D) only.