Reading Material (Mutual inductance)

What is
mutual
Induction?

A process of producing
an induced E.M.F in one
coil due to the change of
current in another coil.

2

Mutual inductance is the This is a
ratio of induced E.M.F sample
in a circuit to the rate text. Insert
of change of current in your
the other circuit. desired
text here.
1

M = ε1 2

 dI2  4

 dt  SI Unit
Mutual Inductance, M : Henry (H)
Induced E.M.F. , 1 : Volt (V)

Rate of current Flow, : Ampere

per second (As-1) 3

3. 2. Current and
This causes magnetic field
increase.
the
INDUCED 0
CURRENT
1. The switch
at the of the circuit
neighboring is closed.

coil. 4

C2 C1

0

5

0 By Faraday’s law: C2
will generate
When the induced E.M.F.
current
starts to 1 2 3 44 The
production
flow in C1, The change of flux will of induced
magnetic also be experienced by E.M.F. in C2
flux will is caused by
begin to C2. the changing
build up of current
inside it. in C1

MUTUAL INDUCTION:

01 Induced E.M.F, 2 in C2 always
1
proportional to, in C1.

02 If current in C1 changes at a

rate of .

03 Thus, C2 experiences a flux
change, .

Induced E.M.F. in C2:

- sign : (1)
Lenz’
law Where

M21 : mutual inductance of
C2 with respect to C1

Iinduced will oppose the change in I1

According to Faraday’s Law, (2)
E.M.F induced in C2 is:

1

Formula for Combining

Mutual 3 equation (1)
inductance
2 and (2):

Same goes if there is a change in current in
C2 and induction in C1.

C1 C2

0

Both expressions for ε1 and ε2, have the same value of M.

10

and

Where
M = Mutual Inductance
N1 = number of turns in C1
N2 = number of turns in C2
Φ1 = magnetic flux in C1
Φ2 = magnetic flux in C2
I1 = current in C1
I2 = current in C2

11

A long solenoid l N1
with cross A N2
12
sectional area, A
and N1 turn is
surrounded at
its center by a
coil with N2
turns.

Current, I1 flows in the
solenoid. The uniform
magnetic field generated at
its center is;

The magnetic flux linkage

through coil caused by the

magnetic field of solenoid is;
µ0 N1I1
Φ2 = B1 A = A
l

13

The Mutual Inductance of coil and
solenoid is;

M = N2Φ2
I1

where

μo : permeability of the free space
N1 : number of turns in solenoid
N2 : number of turns in coil
l : length of solenoid (m)

A : cross sectional area of solenoid (m2)

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