



Section summary
 Inductance is the property of a device that tells how effectively it induces an emf in another device.
 Mutual inductance is the effect of two devices in inducing emfs in each other.
 A change in current
$\mathrm{\Delta}{I}_{1}/\mathrm{\Delta}t$ in one induces an emf
${\text{emf}}_{2}$ in the second:
${\text{emf}}_{2}=M\frac{\mathrm{\Delta}{I}_{1}}{\mathrm{\Delta}t}\text{,}$
where
$M$ is defined to be the mutual inductance between the two devices, and the minus sign is due to Lenz’s law.
 Symmetrically, a change in current
$\mathrm{\Delta}{I}_{2}/\mathrm{\Delta}t$ through the second device induces an emf
${\text{emf}}_{1}$ in the first:
${\text{emf}}_{1}=M\frac{\mathrm{\Delta}{I}_{2}}{\mathrm{\Delta}t}\text{,}$
where
$M$ is the same mutual inductance as in the reverse process.
 Current changes in a device induce an emf in the device itself.
 Selfinductance is the effect of the device inducing emf in itself.
 The device is called an inductor, and the emf
induced in it by a change in current through it is
$\text{emf}=L\frac{\mathrm{\Delta}I}{\mathrm{\Delta}t}\text{,}$
where
$L$ is the selfinductance of the inductor, and
$\mathrm{\Delta}I/\mathrm{\Delta}t$ is the rate of change of current through it. The minus sign indicates that emf opposes the change in current, as required by Lenz’s law.
 The unit of self and mutual inductance is the henry (H), where
$\mathrm{1\; H}=1\; \Omega \cdot \text{s}$ .
 The selfinductance
$L$ of an inductor is proportional to how much flux changes with current. For an
$N$ turn inductor,
$L=N\frac{\mathrm{\Delta}\Phi}{\mathrm{\Delta}I}\text{.}$
 The selfinductance of a solenoid is
$L=\frac{{\mu}_{0}{N}^{2}A}{\ell}\text{(solenoid),}$
where
$N$ is its number of turns in the solenoid,
$A$ is its crosssectional area,
$\ell $ is its length, and
${\text{\mu}}_{0}=\mathrm{4\pi}\times {\text{10}}^{\text{\u22127}}\phantom{\rule{0.25em}{0ex}}\text{T}\cdot \text{m/A}\phantom{\rule{0.10em}{0ex}}$ is the permeability of free space.
 The energy stored in an inductor
${E}_{\text{ind}}$ is
${E}_{\text{ind}}=\frac{1}{2}{\text{LI}}^{2}\text{.}$
Conceptual questions
How would you place two identical flat coils in contact so that they had the greatest mutual inductance? The least?
How would you shape a given length of wire to give it the greatest selfinductance? The least?
Verify, as was concluded without proof in
[link] , that units of
$\text{T}\cdot {\text{m}}^{2}/A=\Omega \cdot \text{s}=\text{H}$ .
Problems&Exercises
Two coils are placed close together in a physics lab to demonstrate Faraday’s law of induction. A current of 5.00 A in one is switched off in 1.00 ms, inducing a 9.00 V emf in the other. What is their mutual inductance?
If two coils placed next to one another have a mutual inductance of 5.00 mH, what voltage is induced in one when the 2.00 A current in the other is switched off in 30.0 ms?
The 4.00 A current through a 7.50 mH inductor is switched off in 8.33 ms. What is the emf induced opposing this?
A device is turned on and 3.00 A flows through it 0.100 ms later. What is the selfinductance of the device if an induced 150 V emf opposes this?
Starting with
${\text{emf}}_{2}=M\frac{\mathrm{\Delta}{I}_{1}}{\mathrm{\Delta}t}$ , show that the units of inductance are
$(\text{V}\cdot \text{s})\text{/A}=\Omega \cdot \text{s}$ .
Camera flashes charge a capacitor to high voltage by switching the current through an inductor on and off rapidly. In what time must the 0.100 A current through a 2.00 mH inductor be switched on or off to induce a 500 V emf?
A large research solenoid has a selfinductance of 25.0 H. (a) What induced emf opposes shutting it off when 100 A of current through it is switched off in 80.0 ms? (b) How much energy is stored in the inductor at full current? (c) At what rate in watts must energy be dissipated to switch the current off in 80.0 ms? (d) In view of the answer to the last part, is it surprising that shutting it down this quickly is difficult?
(a) 31.3 kV
(b) 125 kJ
(c) 1.56 MW
(d) No, it is not surprising since this power is very high.
(a) Calculate the selfinductance of a 50.0 cm long, 10.0 cm diameter solenoid having 1000 loops. (b) How much energy is stored in this inductor when 20.0 A of current flows through it? (c) How fast can it be turned off if the induced emf cannot exceed 3.00 V?
A precision laboratory resistor is made of a coil of wire 1.50 cm in diameter and 4.00 cm long, and it has 500 turns. (a) What is its selfinductance? (b) What average emf is induced if the 12.0 A current through it is turned on in 5.00 ms (onefourth of a cycle for 50 Hz AC)? (c) What is its inductance if it is shortened to half its length and counterwound (two layers of 250 turns in opposite directions)?
(a) 1.39 mH
(b) 3.33 V
(c) Zero
The heating coils in a hair dryer are 0.800 cm in diameter, have a combined length of 1.00 m, and a total of 400 turns. (a) What is their total selfinductance assuming they act like a single solenoid? (b) How much energy is stored in them when 6.00 A flows? (c) What average emf opposes shutting them off if this is done in 5.00 ms (onefourth of a cycle for 50 Hz AC)?
When the 20.0 A current through an inductor is turned off in 1.50 ms, an 800 V emf is induced, opposing the change. What is the value of the selfinductance?
How fast can the 150 A current through a 0.250 H inductor be shut off if the induced emf cannot exceed 75.0 V?
Integrated Concepts
A very large, superconducting solenoid such as one used in MRI scans, stores 1.00 MJ of energy in its magnetic field when 100 A flows. (a) Find its selfinductance. (b) If the coils “go normal,” they gain resistance and start to dissipate thermal energy. What temperature increase is produced if all the stored energy goes into heating the 1000 kg magnet, given its average specific heat is
$\text{200 J/kg\xb7\xbaC}$ ?
(a) 200 H
(b)
$\text{5.00\xbaC}$
Unreasonable Results
A 25.0 H inductor has 100 A of current turned off in 1.00 ms. (a) What voltage is induced to oppose this? (b) What is unreasonable about this result? (c) Which assumption or premise is responsible?
Questions & Answers
nano basically means 10^(9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
how to know photocatalytic properties of tio2 nanoparticles...what to do now
it is a goid question and i want to know the answer as well
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
what is fullerene does it is used to make bukky balls
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
so some one know about replacing silicon atom with phosphorous in semiconductors device?
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
for screen printed electrodes ?
SUYASH
What is lattice structure?
of graphene you mean?
Ebrahim
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
what's the easiest and fastest way to the synthesize AgNP?
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
I'm interested in nanotube
Uday
what is nanomaterials and their applications of sensors.
what is system testing?
AMJAD
preparation of nanomaterial
how to synthesize TiO2 nanoparticles by chemical methods
Zubear
what's the program
Jordan
how did you get the value of 2000N.What calculations are needed to arrive at it
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Source:
OpenStax, Electricity physics. OpenStax CNX. Apr 16, 2013 Download for free at http://legacy.cnx.org/content/col11514/1.1
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