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By the end of this section, you will be able to:
  • Correlate two nearby circuits that carry time-varying currents with the emf induced in each circuit
  • Describe examples in which mutual inductance may or may not be desirable

Inductance is the property of a device that tells us how effectively it induces an emf in another device. In other words, it is a physical quantity that expresses the effectiveness of a given device.

When two circuits carrying time-varying currents are close to one another, the magnetic flux through each circuit varies because of the changing current I in the other circuit. Consequently, an emf is induced in each circuit by the changing current in the other. This type of emf is therefore called a mutually induced emf , and the phenomenon that occurs is known as mutual inductance ( M ) . As an example, let’s consider two tightly wound coils ( [link] ). Coils 1 and 2 have N 1 and N 2 turns and carry currents I 1 and I 2 , respectively. The flux through a single turn of coil 2 produced by the magnetic field of the current in coil 1 is Φ 21 , whereas the flux through a single turn of coil 1 due to the magnetic field of I 2 is Φ 12 .

Figure shows the cross sections of two coils. In each one, the cross sections of the wire of the coil are shown as two circles, one at the top and the other at the bottom. Dots in the upper circles and crosses in the lower ones indicate the direction of flow of current. Coil 1 has field lines labeled B1 passing from between the two circles, going right. Some of these pass through coil 2, which is smaller than coil 1.
Some of the magnetic field lines produced by the current in coil 1 pass through coil 2.

The mutual inductance M 21 of coil 2 with respect to coil 1 is the ratio of the flux through the N 2 turns of coil 2 produced by the magnetic field of the current in coil 1, divided by that current, that is,

M 21 = N 2 Φ 21 I 1 .

Similarly, the mutual inductance of coil 1 with respect to coil 2 is

M 12 = N 1 Φ 12 I 2 .

Like capacitance, mutual inductance is a geometric quantity. It depends on the shapes and relative positions of the two coils, and it is independent of the currents in the coils. The SI unit for mutual inductance M is called the henry (H)    in honor of Joseph Henry (1799–1878), an American scientist who discovered induced emf independently of Faraday. Thus, we have 1 H = 1 V · s/A . From [link] and [link] , we can show that M 21 = M 12 , so we usually drop the subscripts associated with mutual inductance and write

M = N 2 Φ 21 I 1 = N 1 Φ 12 I 2 .

The emf developed in either coil is found by combining Faraday’s law    and the definition of mutual inductance. Since N 2 Φ 21 is the total flux through coil 2 due to I 1 , we obtain

ε 2 = d d t ( N 2 Φ 21 ) = d d t ( M I 1 ) = M d I 1 d t

where we have used the fact that M is a time-independent constant because the geometry is time-independent. Similarly, we have

ε 1 = M d I 2 d t .

In [link] , we can see the significance of the earlier description of mutual inductance ( M ) as a geometric quantity. The value of M neatly encapsulates the physical properties of circuit elements and allows us to separate the physical layout of the circuit from the dynamic quantities, such as the emf and the current. [link] defines the mutual inductance in terms of properties in the circuit, whereas the previous definition of mutual inductance in [link] is defined in terms of the magnetic flux experienced, regardless of circuit elements. You should be careful when using [link] and [link] because ε 1 and ε 2 do not necessarily represent the total emfs in the respective coils. Each coil can also have an emf induced in it because of its self-inductance (self-inductance will be discussed in more detail in a later section).

Questions & Answers

what are waves
KENNETH Reply
In physics, mathematics, and related fields, a wave is a propagating dynamic disturbance (change from equilibrium) of one or more quantities
Abdikadir
Discuss how would orient a planar surface of area A in a uniform electric field of magnitude E0 to obtain (a) the maximum flux and (b) the minimum flux through the area.
KARAN Reply
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Marcel
Find the net capacitance of the combination of series and parallel capacitors shown belo
jean Reply
what is ohm?
Sharafat Reply
calculate ideal gas pressure of 0.300mol,v=2L T=40°c
Viola Reply
what is principle of superposition
Jyoti Reply
what are questions that are likely to come out during exam
King Reply
what is electricity
Jyoti Reply
watt is electricity.
Adam
electricity ka full definition with formula
Jyoti
If a point charge is released from rest in a uniform electric field will it follow a field line? Will it do so if the electric field is not uniform?
Sadaqat Reply
Maxwell's stress tensor is
Ami Reply
Yes
doris
neither vector nor scalar
Anil
if 6.0×10^13 electrons are placed on a metal sphere of charge 9.0micro Coulombs, what is the net charge on the sphere
Rita Reply
18.51micro Coulombs
ASHOK
Is it possible to find the magnetic field of a circular loop at the centre by using ampere's law?
Rb Reply
Is it possible to find the magnetic field of a circular loop at it's centre?
Rb Reply
yes
Brother
The density of a gas of relative molecular mass 28 at a certain temperature is 0.90 K kgmcube.The root mean square speed of the gas molecules at that temperature is 602ms.Assuming that the rate of diffusion of a gas in inversely proportional to the square root of its density,calculate the density of
Gifty Reply
A hot liquid at 80degree Celsius is added to 600g of the same liquid originally at 10 degree Celsius. when the mixture reaches 30 degree Celsius, what will be the total mass of the liquid?
Gifty
Under which topic
doris
what is electrostatics
Yakub Reply
Study of charges which are at rest
himanshu
Practice Key Terms 3

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Source:  OpenStax, University physics volume 2. OpenStax CNX. Oct 06, 2016 Download for free at http://cnx.org/content/col12074/1.3
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