When the switch is closed current begins to
flow in the direction shown producing the
magnetic field B. The current does not
increase to its final value immediately due
the induced E in the loops.
B
I
During the time that the current changes
both the field B and flux through the
coils change. The changing flux
produces an induced E.
EE
According to Lenz’s Law the direction of the induced current
produces an induced field that opposes the change in flux that
occurs.
Eind
Bind
B
Iind
E
I
The directions of the induced field Bind
and the induced current Iind are shown.
The induced Emf, Eind, acts like a battery in
series with the actual battery but its high and
low potential sides are reversed since it is
creating an induced current in the opposite
direction.
The net potential difference applied to the coil is reduced by
Faraday induction and the net current is reduced.
In order to study this phenomenon in more detail it is
convenient to introduce the concept of self inductance (L).
1
Self Inductance
B
Φ - magnetic flux through one loop
Φtotal - total flux through all loops
N loops
Φtotal = NΦ
I
E
The flux depends directly on B which in turn depends directly on the
current in the coils.
Φ total ∝ I
⇒
N Φ = LI
NΦ
The proportionality constant (L) is called the “self inductance”
L=
and depends on the geometry of the coils. Its value is found from:
I
LI
E =−
The induced E is:
dΦ total
d ( NΦ )
dI
=−
= −L
dt
dt
dt
Units for inductance: Henry (H).
l
B
Self Inductance of a Long Coil
A
N loops
I
From Ampere’s law the field inside the
coil is:
µ NI
B=
Φ = BA cos 0 =
The flux through one coil is:
The self inductance is:
L=
0
l
µ 0 NAI
l
NΦ µ 0 N 2 AI µ 0 N 2 A
=
=
I
Il
l
2