NOTA-Mutual inductance

MUTUAL
INDUCTANCE

1

What is
mutual
Inductance?

2

M = ε1

 dI 2 
 dt 

SI Unit: Henry (H) 3

3. 2. Current
This causes and
the induced
current at magnetic
field
the
neighboring increasing.

coil. 0

1. Close the switch.

4

C2 C1

0
5

When the current starts to flow in
C1, magnetic flux will begin to build
up inside it.

The change of flux will also be
experienced by C2.

By Faraday’s law: C2 will generate
induced e.m.f.

The production of induced e.m.f. in
C2 is caused by the changing of
current in C1.

6

MUTUAL INDUCTION:

Induced e.m.f in C1 always
1
proportional to, in C2.

If current in C1 changes at

a rate of .

Thus, C2 experiences a flux
change, .
7

Induced e.m.f. in coil 2: 8

(1)

Where

M21 : mutual inductance of
coil 2 with respect to coil 1

‘-’ sign : Lenz’ law => Iinduced will
oppose the change in I1

According to Faraday’s Law,
e.m.f induced in 2nd coil is:

(2)

Combining equation (1) and (2):

9

C1 C2 C2

0

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

10

and

11

Coaxial coil and a solenoid

l

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

12

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 14

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

A : cross sectional area of solenoid

Now, you have
learned about

mutual
inductance. Let’s

go inside and
don’t forget to

warm up.

15