- Magnitude of
- Induced Electric field
A time varying magnetic field always produces an
electric field. The electric field that will be produced
is given by
E×dl -d B
dt
E
The magnetic field at all points with in the cylindrical
region whose cross-section is indicated in the
accompanying figure starts increasing at a constant
rate ' '. The magnitude of electric field as a
function of r is given as follows.
(I) For r < R
2 2
r dB r
E
dt
E r
(II) For r = R
R
E
2
(III) For r > R
2
2
E R
r
1
Eout r
- Self induction
Self inductance is defined as the induction of a
voltage in a current carrying wire when the current
in the wire itself is changing.
(I) Solenoid
The mean radius of the solenoid is r.
The magnetic field inside solenoid B nI 0
The magnetic flux linked is =NBA, where N
is total number of turns in length l of solenoid.
Self-inductance L 0 n Al^2
I
=
2
0 N A
l
Where (N=nl)
(II)Toroid
A toroid of very large radius r is taken so that
the difference between the outer and inner radii
can be neglected. The total number of turns
are equal to N. The magnetic field at a distance
r from the centre is
B oNi / 2 r
Flux through the toroid
B NA
2
oN iA
2 r
,
The self-inductance
2
L oN A
I 2 r
- Energy stored in an inductor
i
U 0 Li di
U^1 Li^2
2
For a solenoid
2
L^0 N A
l
2
0
U^1 B V
2
2
0
U u B
V 2
- Mutual Induction
The phenomenon of production of e.m.f. in a coil
when the current in neighbouring coil changes is
called mutual induction.
1 i 2 & 2 i 1
1 Mi 2 & 2 Mi 1
M - is same for a given pair of coils.
1 Mdi^2 & 2 Mdi^1
dt dt
- Equivalent Inductance
(I) Equivalent inductance(when M=0)
L L L 1 2
- Induced Electric field
- Magnitude of
- Self induction
- Energy stored in an inductor
- Mutual Induction
- Equivalent Inductance
1 2
1 1 1
L L L
