Consider an electric charge at rest so that at a point P some distance away, we have an electric field but no magnetic field. Let, at time t = 0, an impulse be given to the charge such that it starts moving with some finite velocity. For a moving charge, we expect at P both electric and magnetic fields, but we cannot immediately decide whether the magnetic field at P will change from zero to a finite value instantaneously at t = 0 or after some time.
Instantaneous change means infinite rate of change. If the change is instantaneous at all points then considering any loop, we will conclude from Faraday's law that an infinite e.m.f. and infinite electric field is set up. This in turn would imply an infinite magnetic field as seen from the result. Fields are always finite away from charges and clearly the situation just described is inconsistent with known laws of electricity and magnetism.
\(\oint \overrightarrow B . \overrightarrow {dl} = \mu_0\varepsilon_0 \frac{d\phi_e}{dt}\)
The moving charge sets up a magnetic field in its neighbourhood which in turn creates an electric field in the neighbourhood. The process continues since both time-varying electric and magnetic fields act as sources of each other. Thus an electromagnetic wave is started when a charge is accelerated. It is only when the wave reaches the point P that the magnetic field at P changes.
This shows that an accelerated charge emits an electromagnetic wave. It can also be shown that the electromagentic wave and the oscillator will have the same frequency.
