Faraday's law Definition and 268 Threads

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. E

    Charges pushed to the ends of a pole -- Faraday's law

    Homework Statement We put a pole with a length of 0.2m in a magnetic field equals to 0.4T and move it with a velocity of 4m/s. What is the value of the charges that accumulate in the ends of the pole? Homework Equations E=Bv ε=El The Attempt at a Solution I know that E=1.6V/M and ε=0.32V (Book...
  2. C

    Faraday's Law and Stokes Theorem

    Homework Statement Homework Equations Stokes Theorem The Attempt at a Solution I'm having a tough time "cancelling" out integrals from both sides of an equation (if possible). On the right hand of the equation, we know since it is a closed curve, that Stoke's Theorem applies and we can...
  3. S

    Understanding PhET simulation (Faraday's law)

    Homework Statement I am supposed to make a project based on this simulation, I am trying to see what is happening: https://phet.colorado.edu/en/simulation/faraday If I go to the "Transformer" tab, I have an electromagnet and a circuit consisting of a loop of wire and a light bulb. I can...
  4. D

    Magnetic flux in tap changing transformers

    Hi guys, Non engineer here trying to understand an engineering principle. I think I must be going wrong somewhere in my thought process. 1. Faraday tells us that the EMF generated in the secondary of a transformer is equal to the change in magnetic flux divided by the change in time. 2. The...
  5. astrocytosis

    Induced current in a loop of wire when straight wire is cut

    Homework Statement A square loop, side a, resistance R, lies a distance s from an infinite straight wire that carries current I (pointing to the right). Now someone cuts the wire, so I drops to zero. In what direction does the induced current in the square loop flow, and what total charge...
  6. P

    How does the differential form of Faraday's law relate to induced current?

    Homework Statement I'm in a class where we have to essentially learn E&M ourselves and I'm challenged by Maxwells equations. I'm studying out of Purcell's E&M. The differential form of Faradays law for Maxwells equations is curl E = -∂B/∂t Im having trouble interpreting what to make of this...
  7. Marcin H

    Lenz's Law and Faraday's Law clarification

    Homework Statement This isn't a problem, but I wanted to get some clarification of Lenz's law and Faradays law. So if you have a solenoid of wiresand you take a magnet and move it through the solenoid with a velocity v that magnet will induce a current into the wire according to the right hand...
  8. T

    Faraday's law -- circular loop with a triangle

    Homework Statement A circular coil with radius a is connected with an equilateral triangle on the inside as shown in the figure below. The resistance for each section of the wire is labeled. A uniform magnetic field B(t) is pointing into the paper, perpendicular to the plane of the coil. B(t)...
  9. H

    Faraday's law with Calc 3 integration help

    Homework Statement Suppose an infinitely long wire carrying current ##I=sin_0(\omega t)## is a distance ##a## away from a equilateral triangular circuit with resistance ##R## in the same plane as shown in the figure. Each side of the circuit is length ##b##. I need to find the induced voltage...
  10. B

    Magnetic Flux Questions from Japanese University Exam Papers

    Hello everyone, This is my first post here Firstly, I'd like to start by saying that it's my best intention to follow the rules on this forum. Therefore, if I've posted this in the wrong section please forgive me, I will try and learn the ropes quickly. One of my students has given me some...
  11. H

    Faraday's Law: Induced Voltage and Current in a Loop with Resistance R

    Homework Statement An infinitely long wire carries current I=I_0sin(wt). A distance a from this wire is an w by l loop with resistance R with induced voltage V and induced current i. Find the induced voltage and current in the loop. Homework Equations Faraday's law is given by \varepsilon =...
  12. Pushoam

    Faraday's law of electromagnetic induction -- Motional EMF

    There is magnetic field in B = B ##\hat z## in a region from x=0 to x=l. There is a metal rectangular wire loop with length l and width w in x- y plane with coordinates of four corners as (0,0),(0,w),(l,0),(l,w). This loop is moved with velocity v=v##\hat x##. Now according to Faraday's law...
  13. G

    Why is EMF (ElectroMotive Force) equal to a voltage?

    Hello. Let's say a current i(t) flows through an inductor of solenoid type. Time-varying i(t) generates a magnetic field B(t) inside the magnetic core of the inductor. As B(t) is time-varying, EMF, which is the line-integral of the induced electric field E(t) along a coil (which carries i(t))...
  14. G

    Some confusion of Faraday's law of induction.

    Hello. I have several confusions regarding Faraday's law of induction. EMF = \int_{}^{} {\vec E \cdot d\vec l} = - \frac{{d\Phi }}{{dt}} = - \frac{d}{{dt}}\int_{}^{} {\vec B \cdot d\vec S} . It means that If the magnetic flux Φ through the closed conducting loop changes in time, electric...
  15. G

    Transformer equation: Using Faraday's law "the wrong way"?

    Hi. All derivations of the (ideal) transformer equation ##\frac{U_p}{U_s}=\frac{n_p}{n_s}## use Faraday's law of induction $$U=-n\cdot \frac{d\Phi}{dt}$$ for primary and secondary and equate the change of flux ##\frac{d\Phi}{dt}##. Until now, in my textbooks it was always like this: Electrical...
  16. Tobi

    Faraday's law or Lorenzt force?

    A student in my physics class posted, in a group, a wrong answer to a question. The situation was: A plane has a wire extended between the tips of its wings and flies through a magnetic field, perpendicularly, while accelerating. The question was: What will be the induced current? His answer...
  17. S

    Solving Faraday's Law Problem: Finding EMF Needed to Stop Current at Middle R

    Homework Statement If I have the circuit below, and the white circle is Infinite Coil with current of I=xt, Counterclockwise, with a radius a. from Faraday's law we know that will be Electromotive force . 2. Homework Equations what the EMF in needed to stop the current at the middle R ? The...
  18. G

    Faraday's law for constant velocity, area and B-field

    Hi. If a planar wire loop is moved through a homogeneous magnetic field (field lines perpendicular to the loop plane) with constant velocity and no rotation, Lorentz force will move some electrons to one side of the loop, creating a potential difference. But how does this work with Faraday's...
  19. Biker

    Induced EMF in a circle: Faraday's law

    Homework Statement Explain what happens in the following situation: You have a loop in the form of a circle and there is a varying magnetic field inside that loop as the following picture illustrates: Homework Equations Faraday's law lorentez force The Attempt at a Solution I first thought...
  20. Conductivity

    How does Faraday's law include self inductance?

    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...
  21. J

    Struggling to understand what Faraday's law says

    Faraday's law talks about the change in the flux through a loop, but I never see how people take into account the change in the flux due to Faraday's law itself and I am wondering if that leads to a contradiction. For example when calculating the current through a physical loop with area A and...
  22. Mzzed

    Voltages in an induced current

    I've been messing around with ampere's and faraday's laws as we have recently been applying them in undergrad level physics. I'm confused as to how voltage fits in with these laws when used for a solenoid inducing a current in a material placed inside the solenoid. I know that the induced...
  23. S

    Spatial derivative of Electric Field in Faraday's Law?

    According to Faraday's Law, Time-Changing magnetic field creates an induced current in a closed conducting loop. This is the equation: ##\nabla \times \mathbf{E} = -\frac{\partial \mathbf{B}} {\partial t}## 1-) Does this current (##\nabla \times \mathbf{E} ##) have to be an alternate...
  24. DoobleD

    Partial or total derivative in Faraday's law

    I just realized there's a little difference between the differential and integral forms of Faraday's law I didn't notice earlier. In the differential form, it is the partial time derivative that is written, while in integral form, it is simply the time derivative. Why is that ?
  25. Peter2

    Faraday's Law of Induction - Experiment Giving Weird Results?

    Homework Statement [/B] Hi everyone, some school mates sugested id try this forum for help with this work i have :) - will try to keep it short We were trying to induce current in a coil and confirm the experimental results with math, but the math is way off and nobody is sure...
  26. Domenico94

    A Gravitational law of induction

    By reading on the internet I ve found various websites talking about the relation between gravitation and electromagnetism, and in particular, under: - "Small" Gravitational fields -"small" changes in energy with respect to time, The linearized enstein' s field equation becomes pretty much...
  27. cnh1995

    Faraday's law and motional EMF paradox

    Consider the diagram below (sorry for the quality:frown:). The circle is the front view of a cylindrical iron rotor (highly ferromagnetic, very low reluctance). The orange part is a single turn of a conductor (very high reluctance) wound around the rotor body. The grey lines are magnetic field...
  28. cnh1995

    Understanding Faraday's Law: Exploring Induced EMF in Rotating Loops

    When a loop rotates in a magnetic field, does it have to actually "cut" the field lines in order to have emf induced in it? I mean if the loop is rotating and there is a rate of change of flux in the loop, does this mean that the loop is also "cutting" the field lines? I know if the loop is...
  29. N

    Faraday's law of electromagnetism

    I have a confusion regarding Faraday's law of electromagnetism. Consider this diagram At this instant, the velocity of the rotor is parallel to the field lines, hence, no emf is induced in the rotor. Altetnatively, we can say that the rate of change of flux associated with the rotor is 0 at...
  30. Quadrat

    Induced emf in various rectangular loops

    Homework Statement [/B] Three conducting loops, all with the same resistance ##R## move towards a uniform and constant magnetic field, all with the same velocity ##v##. Their relative sizes can be identified by the grid. As the loops move into the magnetic field an induced current begins to...
  31. Astik

    How are Lenz's law and Faraday's law connected?

    I want to know the angle of view from which Lenz's law and Faraday's law can be seen methodically.
  32. L

    Question regarding Faraday's law on induction

    The law states: So, what if the change is flux changes are proportionately equal parts of opposite polarities? Suppose you approach a coil with two magnets on either side of the coil, each set to repel each other's north or south faces; the flux increases, but in equal parts opposite polarity...
  33. G

    "Biot-Savart equivalent" of Faraday's Law?

    This is a repeat of this thread https://www.physicsforums.com/threads/biot-savart-version-of-maxwell-faraday-equation.855423/ That thread was dominated by one verbose poster. I am repeating this thread so as to hear the opinions of others.Ampere's Law can be derived from the Biot-Savart Law...
  34. P

    Confusion with electromagnetism and Faraday's law

    Hi- Sorry if this is a silly question, but by definition the magnetic flux is given by integral B dot dA. But From Gauss' law for magnetostatics is this not zero around a closed loop? So would that not then imply that the EMF around any closed loop is zero? Obviously I'm missing something, so I...
  35. A

    Calculate Area of Ring in Uniform Magnetic Field | Faraday's Law Problem

    Homework Statement In a uniform magnetic field with induction of 0.1 Teslas - a coil is located perpendicular to the lines of induction (I suppose it's something like a ring of wire, meaning N=1). Resistance = 2 Ohms. What is the area of the "ring" if when the field is switched on - it will...
  36. S

    Electromotive force in a moving bar

    Hi everyone, I've seen in some lecture notes that a moving conducting bar (length of L) in a uniform and constant magnetic field develops an electromotive force (emf) between the 2 edges of the bar. Lets assume that the bar moves to the right (with velocity v) and the magnetic field (B) points...
  37. K

    SAT II Physics -- Induced current in loop (Faraday's law)

    Homework Statement A loop of wire and a bar magnet are moving relative to one another. Which motion in the diagrams shown below will NOT induce a current in the loop? Homework Equations Lenz's Law: A changing magnetic field can induce a current in a direction that produces its own...
  38. S

    Question about Faraday's law of induction

    I was studying the Maxwell equation for Faraday's law: ∇×E = -(∂B/∂t) I then did some math and noticed that the electric field is a conservative vector field, because ∇×E= <0,0,0> Since this is the case, based on the above Maxwell equation this would set the time derivative of the magnetic...
  39. M

    Wrongly applying Faraday's Law to time changing loops

    Faraday's law is $$\nabla \times \mathbf{E} = - \frac{d\mathbf{B}}{dt} $$ If we let our time dependent surface be ##\Sigma(t)## and its boundary ##\partial \Sigma(t)##, then by Stokes' theorem $$ \oint_{\partial \Sigma(t)} \mathbf{E} \cdot d\boldsymbol{\ell} = - \int_{\Sigma(t)} \frac{\partial...
  40. xSpartanCx

    Faraday's law with loop of wire and resistor

    A coil 3.65 cm radius, containing 560 turns, is placed in a uniform magnetic field that varies with time according to B=( 1.20×10^−2 T/s)t+( 3.05×10^−5 T/s4)t^4. The coil is connected to a 600-Ω resistor, and its plane is perpendicular to the magnetic field. You can ignore the resistance of the...
  41. J

    Need help understanding the changing time portion of Faraday's law

    I need infomation on how to calculate the changing time part of Faradays law. The answer i keep coming up with seems very low. I learned on this forum a few years ago, and i believe i have been doing it inproperly. Here is the formula i learned: Use N=100 B=0.4...
  42. S

    Why is Faraday's law one-sided?

    Faraday's law states that the curl of E is equal to the negative of the rate of change of a magnetic field. That means that a changing magnetic field causes a curling electric field. But then, shouldn't the opposite be true? That is, shouldn't an electric field with constant circulation...
  43. N

    Calculate Voltage Output Using Faraday's Law

    so I'm trying to find the voltage output of little wireless power transfer device that I have made (I realize I could just use a Multimeter but where would be the fun in that) V = -N A (dB/dt)from what I have gathered from online research: N = permeability of my core which is like 1 because I'm...
  44. Y

    Calculating Induced EMF using Faraday's Law: A Magnetic Flux Problem Solved

    Homework Statement A magnetic flux of 400 micro-webers passing through a coil of 1200 turns is reversed in 0.1 sec. Calculate the average value of the e.m.f. induced in the coil. (Hint use Faraday's Law) Homework EquationsThe Attempt at a Solution So I know that phi = F/R Wb phi is flux F...
  45. Kostik

    What is the Paradox of Faraday's Law and its Connection to Magnetic Fields?

    There's something very curious about Faraday's Law that results from considering a closed curve in space (and any surface whose boundary is that curve). Forget about conducting wires and EMFs: Faraday's Law gives the result of the integral of E along the curve in terms of the rate of change of...
  46. S

    Faraday's law theoretical question

    This is just a general theoretical question. If i have a piece of wood that is wrapped with coils and then run a current through these coils. Will the magnetic field generated by this cause a voltage in a conductor if it is close enough to it? If this is the case could you explain how that...
  47. DoobleD

    Why Faraday's law works with superconductors?

    1: Faraday's law states that a changing magnetic flux induces a voltage. 2: Voltage is the integral of E field with distance. 3: In a superconductor, or equivalently an with idealized wires having 0 resistance, there can't be any electric field inside. Thus, voltage in a superconductor should...
  48. Kerrigoth

    Calculating multiple magnitudes for induced electric field

    Let's say I place two different size conducting loops inside of a uniform magnetic field. For the sake of the diagram I have the loops share a point, but just treat them as though they are not touching. Then I decrease the value of the magnetic field very quickly. \frac{dB}{dt} =...
  49. Dorian Black

    Faraday's Law for a linearly rising magnetic field

    Hi, Imagine a conductive wire bent to the shape of a loop without its ends meeting. A magnet is moved with respect to the loop such that the magnetic field crossing it (perpendicularly) is linearly increasing with time (Φ=kt) where k is a constant. The induced emf is the rate of change of...
  50. E

    Quick question on direction of dl in motional emf integral

    Homework Statement u = velocity B = magnetic flux density Homework Equations ∫ (uxB)⋅dl The Attempt at a Solution From my understanding, the direction of dl depends on the resulting direction of (uxB). How will I know if my dl is in positive or negative?
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