What is Self inductance: Definition and 42 Discussions
Inductance is the tendency of an electrical conductor to oppose a change in the electric current flowing through it. The flow of electric current creates a magnetic field around the conductor. The field strength depends on the magnitude of the current, and follows any changes in current. From Faraday's law of induction, any change in magnetic field through a circuit induces an electromotive force (EMF) (voltage) in the conductors, a process known as electromagnetic induction. This induced voltage created by the changing current has the effect of opposing the change in current. This is stated by Lenz's law, and the voltage is called back EMF.
Inductance is defined as the ratio of the induced voltage to the rate of change of current causing it. It is a proportionality factor that depends on the geometry of circuit conductors and the magnetic permeability of nearby materials. An electronic component designed to add inductance to a circuit is called an inductor. It typically consists of a coil or helix of wire.
The term inductance was coined by Oliver Heaviside in 1886. It is customary to use the symbol
L
{\displaystyle L}
for inductance, in honour of the physicist Heinrich Lenz. In the SI system, the unit of inductance is the henry (H), which is the amount of inductance that causes a voltage of one volt, when the current is changing at a rate of one ampere per second. It is named for Joseph Henry, who discovered inductance independently of Faraday.
Because I like mathematics，I am still young，so found this forum where I can ask questions about mathematics.I hope to find many people who love mathematics here and make progress here.
Hi all,
I recently fabricated a bunch of gold coils patterned onto a glass substrate and am in need of measuring the inductance of these samples. Since the feature size is in microns, I can't exactly use an RLC meter.
At the moment, I'm trying to build an LCR series circuit with a PCB and...
In Sadiku, he used the formula dλ=dΨ * Ienclosed/I
to determine the total flux linkage for coaxial cable for ρ<a and for a<ρ<b, but I applied this formula for the solenoid and it didn't work, the way that works for the solenoid is by using λ=N*Ψ.
So why we multiply by Ienclosed/I in the coaxial...
The following is my solution to this problem; I would appreciate some feedback, especially on part (b), which I have found the most challenging. Thanks.
(a) Using Ampere's Law I get ##B=\mu_0 n i_1## where ##i_1## is the current through the solenoid, and since ##\phi=Li_1##, where ##L## is the...
In my textbook on EM, the formula for self inductance of a finite solenoid is given as:
L= (μ(o)* N^2*A * {√(a^2+ l^2) - a} )/l^2 where a=Radius of each turn, l=length of solenoid.
I am having trouble and extreme difficulty in trying to ascertain how this formula was derived in the book and...
In the given question they have not provided the dimensions of the coil so I assumed it to be very close to the wire and having negligible dimensions compared to the wire . Then EMF induced in the coil due to the current in the wire comes out as M*a . Which when divided by resistance gives...
Homework Statement
Homework EquationsThe Attempt at a Solution
Self inductance depends on the geometry of the solenoid . It doesn't depend on the sense of windings . So , L1 = L2 .
But I don't understand how to deal with superconducting wires .
Does a superconducting wire affect the...
Homework Statement
Homework EquationsThe Attempt at a Solution
Self inductance L = μ0n2πr2l . This means it depends only on geometrical factors .
So , self inductance in both the cases should be equal .
But if I think in terms of L = Φ/I , then Magnetic field at the center is twice that...
I have found answers on how to calculate the self-inductance of toroid of rectangular cross section, however my question says that "The winding are seen as a thin homogeneous currentlayer around the core" (excuse the translation). What does that mean for N? Does it mean N=1?
The context is an ac circuit with only one element - the inductor. My textbook says that the self-induced emf increases with increasing angular frequency, but I'm having trouble seeing this mathematically. If self-induced emf = ε = -L(dI/dt) and L = X/ω, then emf and ω are inversely related...
Hi Forum
I am trying to get a better grasp of the relation between electric field and the magnetic field.
The overall question is "What is The origin of selfinductance in a current loop?"
Here are my thourghts:
A battery is connected to a say circular wire with some resistance. The current...
Homework Statement
A thin hollow cylinder of radius a is surrounded co-axially by another hollow cylinder of radius b, where b>a. An electric current I flows through them (I is into the plane of paper (x) in outer cylinder and coming out of plane of paper (.) in inner cylinder). Find the:
a)...
Hi.
Superconductors can be made hover above or even below magnets. As far as I know, this can be interpreted as an extreme form of Lenz's law: Eddy currents on the surface of the superconductor create an opposing force that is able to cancel gravity since the currents aren't affected by...
A varying magnetic flux causes an induced voltage (according to Faraday-Lenz law) that generates a current that generates a magnetic field that generates another magnetic flux in the same circuit. Does the Faraday-Lenz law include this self induction? In other words why can't we take that...
Homework Statement
Given two inductors, connected in parallel connected to a battery, why do the following emf relations hold?
$$\mathcal{E}_1 = - N_2 A \frac{d B}{d t} = -M\frac{d I_1}{d t } \\
\mathcal{E}_2 = -L_2 \frac{dI_2}{dt}- M \frac{dI_1}{dt}$$
See attachment !
Homework Equations...
Good evening everyone.
I have a misconception regarding self inductance. I know that back emf induced in an inductor starts with the same value of the original voltage source and then keeps decreasing to reach zero. I also know how this is related to the derivative of current with respect to...
If current I passes through a circular loop of radius R,then what will be the self inductance of that loop?
(calculating flux through the loop leads to calculating magnetic field at every point inside the loop which is an elliptic integral.)
My observation is to verify self inductance formula by measuring the resonant frequencies of different coils in an LC circuit.For this, I am asked to use this formula by my mentor :
L = 1/(4π^2 . f^2 . C)
Here,
f = different resonant frequencies,
C = capacitance of the capacitor in the LC...
In a DC circuit(Yes, keep going), when current starts to flow, and that current needs a bit of time to stabilize to its maximum value. Since there is change in current(increase) there is an increasing magnetic field, a changing flux... that will induce a -V to the circuit. Eventually when...
Homework Statement
Hi again guys, been stuck on this problem for a while now, thought it would be a simple bumping in some values in a given equation question but I can't get the correct answer :confused: Heres the problem:
What is the inductance of a 600 turn coil wound on a core of cross...
Self inductance of a coil : how does it happen ? I've got some hardtime trying to imagine how it happens , the phrase which confused the most while studying was "each turn acts as a small magnet ",so why does it change polarities at the moment of switching the circuit on or off ? Also the whole...
Hello,
I am using a lock-in amplifier to measure the AC voltage across a small sample of superconducting wire located in a cryostat.
As the self-inductance and the capacitance of the wires used for the measurement are non-negligible, I have basically connected the lock-in amplifier in series...
So I know transformers work by mutual inductance. A first loop that is connected to AC current produces an alternating B which produces a changing flux. As a result an induced Emf is formed. This Alternating B is also alternating in the second coil as well to produce same emf (if same number of...
Homework Statement
For one of the problems in my homework it asks to prove that L=μAN^2/length ...i didnt have a problem with that osrt but the second part states a spring is 5cm long and has a diameter of .15 cm with 50 coils...how much self-inductance must you include for it to model as an...
Homework Statement
So in Walter Lewin's Electricity and Magnetism video series:
http://www.youtube.com/watch?v=UpO6t00bPb8&feature=relmfu
At around 10:00 he says that the resistance in the self inductance is zero because self inductance is superconducting material. However is it possible...
Hi, I was reading some text and came across this problem, the problem is also mentioned in this link from Wiki: http://en.wikipedia.org/wiki/Inductance#Self-inductance
They said that it is because the 1/R now becomes infinite, this is what I'm confused about. From my understand, there would be...
Homework Statement
calc the self inductance of a hairpin...to get a definite answer assume the wire has a tiny radius of e
Homework Equations
L=\phi/I
The Attempt at a Solution
So i found the b field \muI/2\pis
than for the flux, I got \muI/2\pi\int1/s Lds
In the book, they got...
Homework Statement
Calculate the self inductance of a solenoid that is tightly wound with a wire of diameter .1 cm , has a cross sectional area of .9 cm2 and is 40 cm long?
Homework Equations
The Attempt at a Solution
the formula L=u0n2V where V=volume and n=number of turns...
Hi all,
The situation is this: I need to calculate the self inductance of two solenoids wired in series, of equal radius and a given separation d. They are coaxial. The length h of each is known.
Most double-solenoid references I found looked at the mutual inductance, and not the...
Homework Statement
demostrate that the self inductance of a selonoid (L) that have: length = "l"; radius= "a" ; number of turns per unit of length= "m" , is:Homework Equations
L = pi*(m2)*(a2)*Uo*[ ( (l2)+(a2) )1/2) - a ]The Attempt at a Solution
It is suposse that the selfinductance is just...
i am having a doubt that when we find a expression for mutual inductance we say that flux change in primary coil induces emf in secondary coil. but why change in flux doesn't induce any current in primary coil also.
http://i26.tinypic.com/250tkyh.jpg
the formula for magnetic field
is like they show but its not divided by l
like they did
i can't see a reason why they present it that way
??
Homework Statement
Give a definition of (self) inductance. Suppose a battery, which supplies a constant EMF ϵ_0 is connected to a circuit of resistance R and inductance L at t = 0. Find an expression for the current as a function of time.
Homework Equations
V = IR
V =...
Homework Statement
A long, solonoidal coil with 2000 turns produces a B field pf 3mT at its center when a current of 1A flows through the coil. If the cross sectional area of the coil is: 2*10^-3 m^-2, and the field is uniform throghout the solonoid, determine the self inductance of the oil...
Homework Statement
Griffiths problem 7.23
Copute the self inducatnce of the hairpin loop shown in the figure. (neglect contribution from ends since mosto f the flux comes form the straight section) To get a definite answer , assume the wire has a tiny radius epsilon, and ignore any flux...
hey,
i was just confused here, which is the right formula for finding the self inductance of a solenoid, given the number of turns, the cross-sectional area, the length, and the current.
is it L = Uo x Ur x N^2 x A / L
(Uo = mu o, Ur = mu r)??
pls if it is wrong, let me know the right...