1.4 V & I or E & H ?
9
1.4.3 Inductors
Although inductors are usually wound around a cylinder or toroid made of specific materials,
at radio frequency, air-core inductors are quite common and in fact sometimes the best solution. For
simplicity we will therefore analyse the field of an air-filled solenoid since this gives us enough of an
insight into the behaviour of electric and magnetic fields to a first approximation.
Figure 1.4-3 Air-core inductors
Using Ampere's law
4
, the field at any position inside the solenoid, may be easily calculated as
Where represents the number of turns for unit length and the current through the solenoid.
The electric field at a distance r from the axis of a solenoid may be derived from Faraday's
law of Induction where the line integral is calculated over a circular path of radius and length
and the magnetic flux over the respective surface
. This is shown in Figure 1.4-4.
Figure 1.4-4 Electric and Magnetic fields inside a solenoid, E is perpendicular to the page and entering it.
∮
4
Ampere's law states that
∮
where the integral is calculated along an Amperian loop which
encloses the total current
2
r A
Circular path
B
B
B
B
E
(1.4-13)
(1.4-15)
(1.4-14)
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