CHAPTER 1 - Fundamentals of Electrical Circuits
10
Combining equations (1.4-15) and (1.4-14) yields
∮
( )
( )
( ) ( )
This shows how, at position , the magnitude of the electric field is related to the first
derivative of the magnitude of the magnetic field in a linear fashion, just like the voltage across an
inductor is related to the first derivative of the current, equation (1.4-1)(c).
Now, before we introduce the inductance , let us see how this quantity comes about. First
of all, we need to calculate the total induced voltage or for a solenoid. To this end we use a
very similar expression to (1.4-15) but, because we are looking at the total across the terminals
of the whole solenoid, we must include all loops and hence multiply the rate of change of flux
(
) by the total number of turns N.
Substituting (1.4-15) and (1.4-13) into (1.4-17)
⁄
The inductance L is defined as
is used to conglomerate several constants into one constant of proportionality which linearly
relates and
⁄
.
Now if we substitute (1.4-19) into (1.4-16), we obtain
( )
( ) ( )
Equation (1.4-20) shows that inductance may be used to relate mathematically the
magnitude of the electric field and the rate of change of the magnitude of the magnetic field inside
an inductor at a specific point in space defined by the radial distance from its axis.
(1.4-16)
(1.4-18)
(1.4-17)
(1.4-19)
(1.4-20)
Conquer Radio Frequency
10 www.cadence.com/go/awr
