Simple Nature - Light and Matter

know that there is a delay in time before a change in the configuration of mass and charge in
one corner of the universe will make itself felt as a change in the forces experienced far away.
We imagine the outward spread of such a change as a ripple in an invisible universe-fillingfield
of force.
As an alternative to our earlier energy-based definition, we can define thegravitational field
at a given point as the force per unit mass exerted on objects inserted at that point, and likewise
theelectric fieldis defined as the force per unit charge. These fields are vectors, and the fields
generated by multiple sources add according to the rules of vector addition.
Therelationship between the electric field and the voltageis
∂V
∂x
=−Ex
∂V
∂y

=−Ey

∂V

∂z

=−Ez,

which can be notated more compactly as a gradient,

E=−∇V.

Fields of force contain energy, and the density of energy is proportional to the square of the

magnitude of the field,

dUg=−

1

8 πG

g^2 dv

dUe=

1

8 πk

E^2 dv

dUm∝B^2 dv

The equation for the energy stored in the magnetic field is given explicitly in the next chapter;
for now, we only need the fact that it behaves in the same general way as the first two equations:
the energy density is proportional to the square of the field. In the case of static electric fields,
we can calculate potential energy either using the previous definition in terms of mechanical
work or by calculating the energy stored in the fields. If the fields are not static, the old method
gives incorrect results and the new one must be used.
Capacitance,C, and inductance,L, are defined as

UC=

1

2 C

q^2

and

UL=

L

2

I^2 ,

measured in units of farads and henries, respectively. The voltage across a capacitor or inductor

is given by

VC=

q

C

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