What is Faraday's law: Definition and 266 Discussions

Faraday's law of induction (briefly, Faraday's law) is a basic law of electromagnetism predicting how a magnetic field will interact with an electric circuit to produce an electromotive force (EMF)—a phenomenon known as electromagnetic induction. It is the fundamental operating principle of transformers, inductors, and many types of electrical motors, generators and solenoids.The Maxwell–Faraday equation (listed as one of Maxwell's equations) describes the fact that a spatially varying (and also possibly time-varying, depending on how a magnetic field varies in time) electric field always accompanies a time-varying magnetic field, while Faraday's law states that there is EMF (electromotive force, defined as electromagnetic work done on a unit charge when it has traveled one round of a conductive loop) on the conductive loop when the magnetic flux through the surface enclosed by the loop varies in time.
Faraday's law had been discovered and one aspect of it (transformer EMF) was formulated as the Maxwell–Faraday equation later. The equation of Faraday's law can be derived by the Maxwell–Faraday equation (describing transformer EMF) and the Lorentz force (describing motional EMF). The integral form of the Maxwell–Faraday equation describes only the transformer EMF, while the equation of Faraday's law describes both the transformer EMF and the motional EMF.

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  1. Blitzmeister

    Induced emf of Sliding Wire Down Rails

    Homework Statement [This is the best image I could find] The link on the bottom part of the rails is now removed creating two parallel wires that are not connected (so no longer U shaped but just two rails). Now a wire of length L, mass m and resistance R slides without friction down parallel...
  2. Y

    Faraday's Law and Motional EMF: Exploring Causes

    is "motional emf "the real explanation for the reason why emf is induced in faraday law?? thanks...
  3. Y

    Why is Magnetic Flux Important in Understanding Induction?

    can someone tell me , why must the magnetic flux be taken into account instead of magnetic field ?? thanks...
  4. R

    Solving Faraday's Law: Circular Loop with Resistance 0.380Ω

    Homework Statement A circular loop of wire with radius 0.0300m and resistance 0.380Ω is in a region of spatially uniform magnetic field, as shown in the following figure(Figure 1). The magnetic field is directed into the plane of the figure. At t = 0, B = 0. The magnetic field then begins...
  5. davidbenari

    Understanding Faraday's Law with Solenoids

    It is a well known fact that whenever we want to calculate the emf in a solenoid we usually multiply the changing flux for one loop times N, which is the number of turns in the solenoid. But why is this? For example, in the case of amperes law, I know that it makes sense to add currents...
  6. Feodalherren

    Faraday's Law - induced emf of a rotating loop

    Homework Statement Consider the loop in the figure below. What is the maximum induced emf in each of the following cases if A = 600 cm2, ω = 31.0 rad/s, and B = 0.490 T? Rotating about x,y,z? Homework Equations Faraday's law The Attempt at a Solution This should be relatively easy since the...
  7. R

    Calculating Voltage Amplitude with Faraday's Law

    Farraday's Law states V= -N.flux/time , if this calculates voltage how does one determine amplitude?
  8. D

    Can I use generalized Stokes' theorem in Faraday's law?

    It is a nonsense use the generalized Stokes' theorem in right side of Faraday's Law? we know this is true...\displaystyle \oint_{\partial \Sigma}\vec{E}\cdot dl=-\int_{\Sigma} \frac{d\vec{B}}{dt}\cdot d\vec{A}\Rightarrow \int_{\Sigma}\vec{\nabla}\times\vec{E}\cdot d\vec{A}=-\int_{\Sigma}...
  9. W

    Faraday's Law and the radius of the coil

    I've only recently started learning basic electrodynamics, but I don't understand why a loop of coil with a small area and a magnet falling through will produce a larger peak to peak emf amplitude than a loop of coil with a larger area with the same magnetic field falling through. To clarify...
  10. I

    Derivation of Faraday's Law from Lorentz's

    $$\vec{F}=q\vec{v}\times\vec{B}$$ $$\frac{d\vec{F}}{dq}=\vec{v}\times\vec{B}$$ $$\int\frac{d\vec{F}}{dq} \cdot ds=\int(\frac{d\vec{s}}{dt}\times\vec{B}) \cdot ds$$ from here, I went about it two different ways: 1.) Here I assumed everything was at right angles and got rid of all the vectors...
  11. A

    Faraday's law for electrostatics

    I recently learned about faraday's law about electromagnetic induction , where you move a piece of magnetic towards and away from a coil of conductor, what if we replaced the magnet with an electret ( electrostatic equivalent to permanent magnet) and we moved it towards and away from a grounded...
  12. I

    Derivation of Faraday's Law of Induction?

    I was wondering if someone could show me the derivation of Faraday's Law of induction from the more fundamental Lorentz Force.
  13. J

    Faraday's Law and Magnetic Flux

    Homework Statement Hi, this is not a homework problem per say but I am just struggling with some concepts related to my homework. I am struggling with the concepts of flux linkage and flux cutting. Are these one and the same thing? The following statement in my book is where my confusion has...
  14. D

    Simple faraday's law problem (phi = what?)

    Homework Statement A toroid with N windings and radius R has cross sectional radius x (x<<R). The current running through the wires is given by ##I = I_0\sin (\omega t)##. There is a magnetic field in the center of the toroid. A loop of wire of radius three times that of the...
  15. D

    What Does the Area in Faraday's Law Represent?

    In the formula: ## emf = -\dfrac{d\phi}{dt}##, ##\phi = \int B\cdot dA##. Does the area mean only the part of the region which has a magnetic field (if it's constant)? for example, if you have a loop around a toroid, and want to calculate the induced emf, would ##\phi = B(\pi radiusoftoroid)^2...
  16. D

    Faraday's law of mutual induction

    When solving for mutual induction, how do you know what surface to take the flux over?
  17. L

    Is the term loop loosely defined in Faraday's law?

    Is the term "loop" loosely defined in Faraday's law? A voltage will be induced in a loop of wire when the magnetic field flux through the loop changes If you're reading this, you probably know what happens when you hook up the leads from an oscilloscope to a microphone. Nothing, lol. There...
  18. D

    Faraday's law of induction with ferromagnets?

    An electromagnet pulls a ferromagnet from a distance(r), now there is a change in flux. The total magnetic field in this case is increases or decreases? From my understanding the alignment of the domains should increase the magnetic field, but it is not noticeable... Now since there is Δ in...
  19. E

    Faraday's Law and electric force

    I'm working on personal research problem while taking leave from school to work a Co-op. The basic idea of what I'm trying to create is a device that will produce electrical charge without having to be charged or have some outside dependence of electric force. the only way I could think to do...
  20. F

    Understanding Faraday's Law: The Role of Magnetic Flux and Imaginary Surfaces

    Hi, please could someone help explain how magnetic flux works in Faraday's law as I struggle with electromagnetism. From what I understand, if you have a loop of wire in a magnetic field then you get an induced current if the flux is both changing and perpendicular to the plane of the loop...
  21. S

    Polarization of Electromagnetic Wave and Faraday's Law of Induction

    Homework Statement Hey guys. I have an electromagnetic wave traveling in the z direction and polarized in the x direction. The frequency is 1 MHz and average power density is 1 W/m^2. An antenna in the shape of a circular wire is in the xy-plane centred at the origin. I would like to use...
  22. V

    Electric Generators and Faraday's Law

    Homework Statement When a generator turns at 60 Hz, the amplitude of the induced EMF is 50 V. What is its amplitude when it turns at 180 Hz if the magnetic field remains the same? Homework Equations ω = 2∏f ε = ε0sin ωt The Attempt at a Solution If f = 180 Hz, ω = 2∏(180 Hz)...
  23. 2

    Understanding Faraday's Law: Investigating Phase Shift in an AC Circuit

    I did an experiment with two solenoids, one inside the other. The inner solenoid was hooked up to an AC power source and ammeter. The outer coil had a voltmeter. This is a faraday's law experiment. Because the current is changing, we can find a formula for the emf. Here are my math steps: So...
  24. C

    Trouble understanding this derivation of Faraday's law

    I am having trouble understanding part of the derivation of Faraday's law given in this lecture at around 57:00 So the first goal is to calculate the change in magnetic flux through a changing closed loop in a dynamic magnetic field, and it's given by the following \phi(t+\Delta...
  25. A

    When will the induced current in the loop be maximal during acceleration?

    Homework Statement A rectangular loop moves with constant speed v towards an area in space with constant magnetic field B (As shown in the attachment). The loop enters this area and leaves it from the other side. Also given: d>c. Assume that t=0 when the left edge of the loop is just on the...
  26. S

    Simple DC motors Current, Torque, EMF and Faraday's Law

    Ok, so I'm doing an experimental write up for an experiment on adjusting voltage on the speed of a simple DC motor, and changing the number of coils. I thought that I understood what I was saying but I've recently become a little confused with the concepts of torque vs speed specifically when...
  27. A

    Faraday's Law - very tricky question

    Homework Statement A straight infinitly long wire with a current of I upwards is stationary. A rectangular loop with length a and height b is moved to the right with constant speed of v across the wire in the plane of the paper. At t=0 the right edge of the loop is exactly at the same location...
  28. G

    Faraday's law on rotating disk

    Homework Statement A metal disk is rotating with constant angular velocity in a constant magnetic field perpendicular to it. Use Faraday's law to fint the the induced voltage difference between the two points on the wire. The attempt at a solution So to use Faraday's Law, I need to...
  29. P

    Confirming Faraday's Law - interference in measurement.

    Hi, Homework Statement We ran an experiment for confirming the linearity of Faraday's Law (the relation between EMF and the rate of change of flux), by plugging a magnet to a motor rotating in the axis of a solenoid (inductor). In my graph of the amplitude of EMF wrt time, I noticed some...
  30. G

    What is the correct orientation for calculating emf using Faraday's law?

    I just did an exercise from the book "a student's guide to Maxwell's Equation". I like the book, because the author has detailed solutions on his website. However, I suspect that his solution is wrong on this one. Problem statement: "A conducting bar descends with speed v down conducting...
  31. O

    Faraday's Law of Induction; Why is it the *enclosed* magnetic flux?

    Hello Reader, Basically in Faraday's law, a change of flux over time induces an EMF. I was wondering why is it the enclosed magnetic flux and NOT the magnetic flux through the conductor that we consider. More specifically, I understand that the flux through a rectangular surface would be...
  32. G

    Faraday's law on circular wire

    In my examples on Faraday's law in my book, they use a drawing of a magnet approaching a circular wire. The changing magnetic flux then induces an emf on the circle of wire, which in turn causes a current to flow. I'm wondering if a current will flow in that wire without it having an element...
  33. K

    My Research Project centered around Faraday's Law: Help and Discussion

    Quick question. I'm currently(started today) working on research centered Faraday's Law with an application in automobiles, and I'm just looking for some good articles/academic journals/research papers on Faraday's law to get a better understanding of it. I gained a brief understanding of the...
  34. L

    Unraveling Faraday's Law: Formal Proof & Understanding the Transformation | Wiki

    Hi, I'm looking for a proof of faraday's law. This is the only page which gives a formal proof of it, but I do not understand the transformation from the first to the second step. It someone could help me out, I would appreciate it. Also, if someone could explain the opposite as well: how do you...
  35. D

    Faraday's law. Induced electric field.

    When you use Faraday's law to calculate the induced electric field due to a changing magnetic flux, you integrate over a loop defined by the circuit you're interested in. Why is the electric field confined to the circuit? Couldn't I just pick a random loop in space and integrate over that...
  36. F

    Faraday's law and gauss's law for magnetism apparent contradiction

    I was reading here https://www.physicsforums.com/library.php?do=view_item&itemid=294 gauss law's for magnetism says ∮B⋅dA = 0 but then faraday's law has d/dt ∮B⋅dA in it. Well if its 0 then d/dt of 0 is 0.
  37. NaOH

    How Does a Voltmeter Respond to Induced EMF in a Circular Wire Loop?

    Homework Statement It is often discussed that a changing magnetic field will create a non-conservative electric field, which would then induces an EMF and hence an induced current, but what happens when we connect voltmeters? Consider putting a circular loop of wire with some resistance in...
  38. U

    How exactly do generators work (Please explain the Faraday's law)

    Hi, everybody! I have done tons of research through the Internet, but still can't understand the Faraday's law and how a generator works. I understand, that inside coils, placed into a rotating magnet, current is generated. But why? What exactly happens to electrons, so they form current...
  39. jaumzaum

    What Does "Distributed" Mean in Faraday's Law?

    Faraday says that a variation of magnetic flux generates an induced emf distributed by the material, which creates eddy currents. I want to know and understand what this "distributed" means. Do we have a constant potential difference between every 2 points of the object? (is this possible?)
  40. I

    Faraday's Law (Flux on one coil due to current through another Coil)

    Homework Statement There are a lot of numbers in this problem. Just about the only way to get it right is to work out each step symbolically first,and then plug numbers into the final symbolic result. Two coils of wire are aligned with their axes along the z-axis,as shown in the...
  41. K

    Definitions for Magnetic flux and Faraday's Law

    I was wondering if my understanding on Magnetic flux and Faraday's law was correct or not, is this okay? Magnetic flux is the number of lines in a magnetic field (Φ) Magnetic field strength (B) is the number of magnetic field lines over a given area B = Φ/A Other names for magnetic field...
  42. 1

    Faraday's Law Need help with explanation

    Homework Statement http://em.groups.et.byu.net/embook/ch6/mod6.4.html ^^The link has the problem Homework Equations The Attempt at a Solution I know the answer is (a), but can someone explain to me the reason configuration (A) induces the largest V emf?? compared to (b) or (c)??
  43. P

    Faraday's Law of Induction - Current in Multiple Wires

    Homework Statement A 7.40 cm diameter coil consists of 15 turns of circular copper wire 2.3 mm in diameter. A uniform magnetic field, perpendicular to the plane of the coil, changes at a rate of 7.29×10^−3 T/s . Determine the current in the loop. Express your answer using two significant...
  44. Y

    Understanding Faraday's Law for Coils: Exploring the Mysterious 10^-8 Multiplier

    For a coil, e=N\frac {d\Phi}{dt} Where e\; is the instantaneous voltage driving the coil and \Phi\; is the flux generated through the coil with N turns. For a coil \oint \vec B \cdot d\vec l =\mu N I \Rightarrow B=\mu N I \Rightarrow \Phi = BS=\mu N I S In the book Handbook of...
  45. L

    Derivation of Faraday's Law from the Lorentz Force Law

    Someone asked me how Faraday's Law of Induction and Ampere's Force Law, both which form part of Maxwell's Equations, are related. Ampere's Force Law is derived from the Lorentz Force Law. They are entirely compatible with Faraday's Law of Induction. Here's how...The Lorentz Force Law states...
  46. D

    Faraday's Law vs Kirchoff's Rule in circuit - nonconservative fields

    I am trying to compare the "relation" conventions used in Kirchoff's Loop Rule with Faraday's Loop Rule. Kirchoff Please go to this MIT OCW link on Kirchoff's Rule and go to page 8/29. Of the four boxes, I would like to point this one Note that the yellow electric field was added...
  47. D

    Same idea, but different approach. Faraday's Law

    Homework Statement The magnitude of $$B$$ is increasing at $$100T/s$$ and the solenoids (the source of the induced EMF) is infinitely long. I want to find the current through the resistors The Attempt at a Solution I basically used the same idea, but I used Mesh's method and I decided to...
  48. C

    Understanding Faraday's Law and Its Effects on Conductors

    When we talk about Faraday's law, we need a change in magnetic flux to create a voltage. So let's say I have a B field that exists in a square region and then a square loop that is a conductor and I push it into the B field. So as I originally push the square loop into the B field I have a...
  49. T

    Resistance in emf - Faraday's Law

    Homework Statement A rectangular wire loop measures 5.00 cm by 8.00 cm, and lies in the plane of the page. It has a resistance of 3.00 Ω. In this region, there exists a uniform magnetic field pointing into the page. Its magnitude, in Tesla, varies according to the equation B(t) = 10.0 −...
  50. T

    Physics Faraday's Law and Induced Electric Fields

    Homework Statement A wire loop with area 8.00 cm2 is placed inside a 20.0 cm long solenoid with 5.00×10^4 turns that carries a current of 1.10 A. The loop is concentric with the solenoid. If the length of the solenoid is stretched so that its length increases at a rate of 8.000e-2 m/s, with...
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