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:

Solution

Physics sir · 3 steps

Ask one thing of each source: is whatever drives the field itself changing with time?

1. The test. A magnetic field comes from a current, or from a changing electric field (displacement current). The field varies with time only if that current or displacement current varies with time.

   ∮ B⃗· dl⃗ = μ₀(I + ε₀ dΦ_E/dt)

   Source	What drives B⃗	Changing in time?	Time-varying B⃗?
   (A) permanent magnet	fixed aligned atomic currents	no	no, static field
   (B) E changing linearly	ε₀ dΦ_E/dt, a constant	no	no, steady field
   (C) direct current	constant I	no	no, steady field
   (D) decelerating charge	moving charge with falling speed	yes	yes
   (E) antenna, digital signal	constant level on each bit	no, in the ideal picture	no, behaves like DC on each level

2. Why (D) works. A moving charge acts like a current proportional to its velocity. When it decelerates, that velocity keeps changing, so its magnetic field keeps changing. This is also why accelerated charges radiate.
3. So. Only the decelerating charge gives a time-varying magnetic field, so the answer is (a), (D) only.

The idea to keep. A changing B⃗ needs a changing source. Constant current or a uniformly changing E⃗ gives a steady field. Only accelerating or decelerating charges make it vary.

Answer from the NTA final answer key. Solution by PrepWiser.