Power system fundamentals - Wind Power Integration: Connection and System Operational Aspects - page 23

of motion - every force has an equal and opposite reaction - that a magnetic field will
exert a force on a current-carrying conductor. This is readily confirmed by experi-
ment. If a conductor carrying current i is placed in a plane normal to the direction of a
magnetic field of flux density B , it is found that the force on the conductor is given by

f / Bli ð 2 : 6 Þ

where l is the length of conductor in the magnetic field. The force is normal to the
field and to the current. Its direction is given by Fleming's left-hand rule, which
may be applied as follows:

f irst finger f ield

m i ddle finger current ( i )

thu m b m otion

It follows from (2.6) that

f ¼ k Bli

where k is a constant of proportionality. The unit of flux density, the Tesla (T), is
chosen such that k is unity, giving

f ¼ Bli ð 2 : 7 Þ

Thus the Tesla (T) is the density of a magnetic field such that a conductor carrying
1 ampere normal to it experiences a force of 1 Newton/m.
Equation (2.7), combined with the definition of the unit of electric current, the
ampere, may be used to determine the permeability of free space, m 0 . The ampere is
defined as 'that current which, flowing in two long, parallel conductors 1 m apart in a
vacuum, produces a force between the conductors of 2 10 7 Newton/m'. From
(2.1) and (2.2), the flux density at one conductor due to the current in the other will be

m 0
2 p

B ¼

The force on this conductor will therefore be, from (2.7),

m 0

2 p ¼ 2 10 7 Newton = m

f ¼

giving

m 0 ¼ 4 p 10 7

Henry = m

2.2.2 Magnetic circuits
It is convenient to deal with electromagnetic systems in terms of magnetic circuits .
A magnetic field may be visualised with the help of flux lines (see Figure 2.1).