Page 44 - Maxwell House

24 Chapter 1

1
9
= = 8.988 ∙ 10 N

4 ∙ 3.1415 ∙ 8.854 1 ∙ 10 −12 ∙ 1000 2
From a mechanical point of view a force ( =ma) can accelerate a heavy truck of m = 50 tons

= 50 000 kg with a = 200 km/s ! So in one second the truck will be 100 km from the traffic
2
lights and an hour will reach a speed of 720,000 km/hour, if it could survive such powerful
push.
Significant charges are not uncommon around us. The Earth bears a negative charge of about
−4.5 ∙ 10 C [15] and our atmosphere accumulates a roughly equal and opposite charge. It is,
5
therefore, no surprise that nature produces so many fireworks, within average 100 lightning
strikes per second! The immense amount of charge that travels through a lightning bolt can
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reach up to 350 C or the charge of 2.18 ∙ 10 electrons with a total mass 2 ∙ 10 −12 kg or only
6 g per year. The age of the Earth is about 4.56 ∙ 10 years. Thus for the whole Earth history
9
lightning would deliver 27 360 tons of electrons. Meanwhile, a single commercially produced
ultracapacitor of 10,000 farads for the wind and the solar power generation system connected
to a 2.7-volt battery stores 27,000 C or the equivalent of 77 of the most powerful lightning
strikes! A compact battery of 17 such capacitors is capable of storing more charges than the
whole Earth.

1.6.7 Electric Field Reality
The equation (1.20) and (1.24) proves the quite remarkable fact that electrical charges store
their potential energy in their surrounding electrical fields. That will bring into play the
conservation energy law: field potential energy can be released and converted into any other
form of energy such as radiant and heat, motion and sound, chemical, you name them. The
electrical fields become quite real: they carry energy and can be measured! For example, the
existence of electric potential implies the transformation of electric field energy into kinetic
energy of movable charges. In other words, electrical potential or pure voltage can be the source
of an electrical current in the material where movable charges such as electrons are not bound
to atomic nucleus or molecules and are free to respond to outside forces created by electrical
fields. Subsequently, the greater voltage means more dominant force, the higher electric current
and more energy to be taken from the electrical sources. However, the movement of a mass of
charged particles that is too big leads to a high probability of collisions between these particles
and the crystal lattice of conductive material and thus an increase in energy loss. That is why a
voltage of 750,000V and higher is used to reduce the transposed mass of charges while
transferring the bulk of electrical energy from power stations to remote consumers. The
potential of several hundred million volts between earth surface and thunderstorm clouds causes
powerful lightning. Shuffling your feet across synthetic carpets might increase your body
electric potential up to 36 000 V. The sparks jumping from your finger are not dangerous but
annoying and sometimes rather painful!

1.6.8 Displacement Vector D. 3 Maxwell’s Equation
rd
Now, we turn to the electric charge conservation law, one of the fundamental laws of physics,
and will demonstrate its association with Gauss’s Law. First of all, let us rewrite Gauss’s law
rd
as the integral form of 3 Maxwell’s equation (see Table 1.7)