



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
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?
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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?
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Starting with
${\text{emf}}_{2}=M\frac{\mathrm{\Delta}{I}_{1}}{\mathrm{\Delta}t}$ , show that the units of inductance are
$(\text{V}\cdot \text{s})\text{/A}=\Omega \cdot \text{s}$ .
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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?
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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.
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(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?
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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
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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)?
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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?
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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)
$\text{5.00\xbaC}$
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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?
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Questions & Answers
how many subject is in physics
the write question should be " How many Topics are in O Level Physics, or other branches of physics.
effiom
how many topic are in physics
Praise
yh I need someone to explain something im tryna solve . I'll send the question if u down for it
a ripple tank experiment a vibrating plane is used to generate wrinkles in the water .if the distance between two successive point is 3.5cm and the wave travel a distance of 31.5cm find the frequency of the vibration
Tamdy
the range of objects and phenomena studied in physics is
straight line motion is called linear motion
linear motion is a motion in a line, be it in a straight line or in a non straight line. It is the rate of change of distance.
Saeedul
your are wrong Saeedul
Richard
Linear motion is a onedimensional motion along a straight line, and can therefore be described mathematically using only one spatial dimension
Jason
is a onedimensional motion along a straight line, and can therefore be described mathematically using only one spatial dimensions.
Praise
what is a classical electrodynamics?
Marga
dynamic is the force that stimulates change or progress within the system or process
Oze
what is the formula to calculate wavelength of the incident light
if a spring is is stiffness of 950nm1 what work will be done in extending the spring by 60mmp
State the forms of energy
Word : Mechanical wave
Definition :
The waves, which need a material medium for their propagation, e.g., Sound waves. \n\nOther Definition: The waves, which need a material medium for their propagation, are called mechanical waves. Mechanical waves are also called elastic waves. Sound waves, water waves are examples of mechanical waves.t Definition: wave consisting of periodic motion of matter; e.g. sound wave or water wave as opposed to electromagnetic wave.h
a wave which require material medium for its propagation
syed
The S.I unit for power is what?
it can be in kilowatt, megawatt and so
Femi
SI.unit of power is.watt=j/c.but kw.and Mw are bigger.umots
syed
study of matter and its nature
Akinpelu
The word physics comes from a Greek word Physicos which means Nature.The Knowledge of Nature. It is branch of science which deals with the matter and energy and interaction between them.
Uniform
why in circular motion, a tangential acceleration can change the magnitude of the velocity but not its direction
because it is balanced by the inward acceleration otherwise known as centripetal acceleration
MUSTAPHA
Tramsmission of energy through a media
Mateo
is the disturbance that carry materials as propagation from one medium to another
Akinpelu
find the triple product of (A*B).C given that A =i + 4j, B=2i  3j and C = i + k
Difference between north seeking pole and south seeking pole
Source:
OpenStax, College physics. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
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