Question

7) What behavior does the classical theory of electromagnetism predict for accelerating charges?

Answer 1

The classical theory of an electromagnetic wave scattered by charged particles, cannot explain low intensity shifts in wavelength: classically, light of sufficient intensity for the electric field to accelerate a charged particle to a relativistic speed will cause radiation-pressure recoil and an associated Doppler shift of the scattered light. However, the effect will become arbitrarily small at sufficiently low light intensities regardless of wavelength. Light must behave as if it consists of particles to explain the low-intensity Compton scattering. Compton's experiment convinced physicists that light can behave as a stream of particle-like objects (quanta) whose energy is proportional to the frequency.

Any accelerated charge particle will emit electromagnetic radiation even an ion when accelerated would give up EM waves. Larmors formula gives the power of the emitted formula in non relativistic frame.

P=q²a²/6pievc³

We know that charges give rise to electric field. The intensity of this field is given by:

E=kq/r²

So the electric field intensity varies inversely to the second power of distance from the charge. We use electric field lines to describe the force experienced by another charge kept at a distance form this charge. For negative charges the force lines/field lines are directed inwards and for positive charges it is directed outwards.Thus its clear that the radiating electric field is dependent on the acceleration.

Classical theory predicted that hot objects would instantly radiate away all their heat into electromagnetic waves. The calculation, which was based on Maxwell's equations and Statistical Mechanics, showed that the radiation rate went to infinity as the EM wavelength went to zero, ``The Ultraviolet Catastrophe''. Plank solved the problem by postulating that EM energy was emitted in quanta with .