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. DocZaius

    Induced EMF through variable-resistance-wire due to Faraday's Law

    Hello, While considering Faraday's Law of Induction, I tried to think of a situation which would expose some difficulties I have with the notion that there is an induced EMF without clear regions of relatively high and low voltage (as in a battery). Here is what I thought would get me started...
  2. B

    How Does the Lorentz Transformation Validate Faraday's Law?

    Homework Statement Use the form of the Lorentz transformation matrix R, and the elcectromagnetic tensor F, and using: \frac{\partial F_{\mu\nu}}{\partial x_{\lambda}}+\frac{\partial F_{\nu\lambda}}{\partial x_{\mu}}+\frac{\partial F_{\lambda\mu}}{\partial x_{\nu}}=0 verify Faraday's...
  3. K

    Solving Faraday's Law for Rotating Loop Motion

    Homework Statement A square loop with sides l is centered on the origin and fixed in the center so it is free to rotate around the x-axis. A magnetic field is changing with time B=B_0(1-exp(-a*t)). I need to find a differential equation to describe the motion of the rotating loop...
  4. B

    Faraday's Law help, not sure if I'm using the equations correctly.

    Homework Statement A coil 3.55 cm radius, containing 480 turns, is placed in a uniform magnetic field that varies with time according to B = (1.20e-2 T/S)t + (3.05e-5 T/s^{4} )t^{4}. The coil is connected to a 620 Ohm resistor, and its plane is perpendicular to the magnetic field. You can...
  5. S

    Lightning according to faraday's law

    Faraday's law applied to lightning, " When lightning occurs air conducts current which happens in Earth's magnetic field will it produce motion in air".
  6. H

    How to apply Faraday's Law of Induction

    Greetings, I have read the explanation on this forum here: https://www.physicsforums.com/showthread.php?t=441637 which discusses Faraday's Law of Induction, but I'm having a hard time understanding how to extrapolate that to my problem. My goal: Construct a circuit that measures ambient...
  7. A

    How Does Faraday's Law Explain Zero Work by Magnetic Forces in Motional EMFs?

    Hello, I am currently trying to really come to grips with electromagnetic induction and Faraday's law. The text I'm using is Young and Freedman's University Physics, 12th edition. How can the emf for a conducting loop moving in a magnetic field be given by the closed loop integral of (v...
  8. B

    Faraday's Law and EMF calculation

    Hi, I found this site with a calculation for EMF: http://www.6pie.com/faradayslaw.php. I just want to see if I have this right. Magnet Surface: Height (0.05 m) * Width (0.004 m) = Area 0.0002 m2. Coil windings: 6 Rotations per second: 5 NdFeB Magnet in N42 (1.33 Tesla) (I will reduce this...
  9. teroenza

    Faraday's Law with square wire

    Homework Statement I have done a few problems with Faraday's law of induction ( closed line integral of E dot dl = -(d/dt)(magnetic flux)). Every time time I have done them, the , albeit simple, problems have used circular wires through which magnetic flux is passing through, and emf is...
  10. K

    Faraday's Law with Acceleration

    I decided to join this forum because we were baffled on the following fact made by a professor. We were hoping to get this cleared up here, since the prof said the math was complicated. Let's assume any arbitrary circuit (forming an area) moving at velocity v through a perpendicular field B...
  11. N

    Finding EMF - why we ignore the negative sign in Faraday's law

    Hi all, I've been using Faraday's law to find the EMF in a coil of wire in a changing magnetic field. EMF = -N (change in mag flux/change in time) for N loops I'm finding that the EMF is always positive regardless of whether the change in flux is positive or negative. I'm wondering at...
  12. teroenza

    Possible title: Surface Error in Faraday's Law Lecture?

    Hello, At approximately 4 min 48 sec. the professor indicates that the surface for the surface integral is closed. This contradicts my albeit limited knowledge in which the magnetic flux through a closed surface is zero (Gauss's law for magnetism). Did he make an error of is my understanding...
  13. F

    Understanding Faraday's Law: -d & dt, E Explained

    Hello, our tutor gave us this equation for Faradays law, but I don't quite understand it's composition. (I have attached a graphic of the equation) Can someone please tell me what the -d and dt represent ? Also, what does the E stand for ? I thought it should be I (current). Thanks kindly for...
  14. S

    Faraday's Law vs. V = vBl for determing potential difference of a conducting rod

    Homework Statement A rod rotates clockwise about a point as pivot with the constant frequency 5 rev/s. Find the potential difference between its two ends, which are 80 cm apart, due to the magnetic field B = 0.3T directed into the page. Homework Equations There are two methods to find...
  15. D

    What is Faraday's Law of Induction?

    Homework Statement #32 Homework Equations faraday's law of induction The Attempt at a Solution umm i don't really understand this concept:frown: so here's my attempt. the answer is C so is it because if you have a wire within a wire and the current of one wire is going one...
  16. A

    Faraday's law of electromagnetic induction

    Homework Statement A flat circular coil with 139 turns, a radius of 5.74 x 10-2 m, and a resistance of 0.502 Ω is exposed to an external magnetic field that is directed perpendicular to the plane of the coil. The magnitude of the external magnetic field is changing at a rate of ΔB/Δt =...
  17. T

    Faraday's law lab report problem with equations and graph(slope)

    Homework Statement the problem is we drew up a graph o E^-3/2(y) against Z^2(x) so the slope is [E^-3/2]/[Z^2]=m we need to rewrite equation three given that z is not equal to zero and then get a final equation like four. we need to isolate (a) so we can determine a value for it using our...
  18. N

    Why does Faraday's law involve a partial vs an ordinary derivative?

    Faraday's law is often stated in SI units as \nabla x E(x,y,z,t) = \frac{\partial B(x,y,z,t)}{\partial t} But x, y, z (or some other set of coordinates) are variables not functions and thus have no "t dependence". So it would seem that the "total derivative" of B is the same as the partial...
  19. P

    Faraday's law and perpetual motion

    If a positive sign were present in Faraday's law instead of a negative sign, this would lead to perpetual motion.. True or false?
  20. P

    Question about faraday's law of induction?

    If a positive sign were present in Faraday's law instead of a negative sign, this would lead to perpetual motion.. True or false?
  21. C

    Faraday's Law: Solving Problem w/ Induced Electric Fields

    Homework Statement A closed metallic square loop with sides with length L is in the xy-plane. The magnetic field varies in the x-direction as B_z = B_0 \sin{\left(\pi x/L\right)}. The loop is being pulled with a constant speed v along the x-direction. a) Determine the emf in the loop by...
  22. A

    How do I apply Faraday's Law of Induction to my project?

    Hey there everyone. I'm working on a project and I want to incorporate a small version of Faraday's Linear Shake Flashlight. I'm stuck on how to apply Faraday's formula to the variables that I have. The formula wants "flux". How to I calculate the flux of my magnets? I know the pull...
  23. D

    Faraday's Law in the frequency domain

    I'm trying to figure out what faraday's law is in terms of frequency rather than time. I think the equation is V = -N*B*A*2f. Where N is the number of turns in the loop, B is the magnetic field, A is the area and f is the frequency. However I am not totally convinced that my derivation is correct.
  24. W

    RL Circuit: Kirchoff's Law is Wrong - Faraday's Law is Correct

    Hi Guys, This is going to be a bit controversial but that's ok. In an RL circuit, both with and without a battery, Kirchoff's law is invoked in virtually every elementary textbook in the United States and perhaps in the world. It is a mistake! The voltage drop across an inductor is...
  25. S

    Faraday's law to find direction of current

    Homework Statement Using Faraday's law, state the direction of current in the loop on the left. (Picture attached) Homework Equations \epsilon = -d\Phi/dt The Attempt at a Solution I know that, assuming the direction of the current on the right side of the loop is from positive...
  26. F

    Does Faraday's Law Hold True in All Inertial Frames?

    Prove that Faraday's Law of electromagnetic induction has the same form in all inertial frames.
  27. T

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  28. S

    Calculating Current in a Rotating Loop Using Faraday's Law

    Homework Statement Plate is rotating on the yz plane, so perpindicular to x-plane. It is rotating at angular velocity, W = 10 [rad/s]. If B = 0.2ay [T] and phi = 0 @ t = 0, find the current i, which is flowing up the portion of the loop that is along the z-axis (current is directed toward...
  29. FeDeX_LaTeX

    Negative Voltage Using Faraday's Law

    Hello; When we use Faraday's Law we can get a negative voltage as a result. What does this mean? I'm guessing it means voltage in the other direction? Thanks.
  30. S

    Understanding Faraday's Law: Implications for Motional EMF Explained

    My textbook said Faradays law EMF = integral of E.dl is only valid if the integration path is stationary. Could someone explain what this means? Does it mean if the conductor changes shape Faraday law is not valid? In motional EMF a conductor moves through a magnetic field and a EMF is...
  31. S

    Faraday's Law - Spatial Varying Magnetic Field Problem

    Homework Statement The figure attached shows a rod of length L = 10 cm that is forced to move a a constant speed of v = 5.00 m/sec along horizontal rails. The rod, rails, and connecting strip at the right form a conducting loop. The rod has a resistance of 0.4 \Omega and the rest of the loop...
  32. C

    Faraday's Law: Conducting rod moving across a magnetic field

    Homework Statement A conducting rod is pulled horizontally with constant force F= 3.40 N along a set of rails separated by d= 0.260 m. A uniform magnetic field B= 0.500T is directed into the page. There is no friction between the rod and the rails, and the rod moves with constant velocity v=...
  33. J

    Faraday's Law and Charge Quantization

    Homework Statement My textbook indicates the following three important points are confirmed by Faraday's law of electolysis: a) matter consists of molecules and molecules consist of atoms b) charge is quantized; only integral numbers of charges are transferred to the electrodes c)...
  34. W

    Faraday's Law not obvious to me

    Hi All, Please take a very long tightly wound solenoid of any radius with another coil wound around the outside of it. Now, if a current is applied to the solenoid, the changing flux of the magnetic field causes an induced emf in the outside coil which is perfectly consistent with the math...
  35. 1

    How Does Faraday's Law Apply to a Non-Uniformly Charged Cylindrical Shell?

    First off, I'm sorry but I am LaTeX illiterate :frown:. Homework Statement An infinitely long conducting cylindrical shell has an inner radius A, an outer radius B, and carries a non-uniform current density J= [2ar]sin(wt) where a and w are constant. What is the magnitude of the induced...
  36. fluidistic

    About another thread, Faraday's law of induction

    Homework Statement Here's the situation: https://www.physicsforums.com/showthread.php?t=363089. First, does a magnetic flux through a rod considered with no surface area makes sense? To reach the result, we have to assume the flux through it to be -BLR since it's going out from the magnetic...
  37. E

    Faraday's law for an infinite magnetic field slab

    Homework Statement The magnitude of an infinite slab of uniform magnetic field is increased. What is the electric field induced by Faraday's Law Homework Equations \nabla \times \mathbf{E} = -\frac{\partial \mathbf{B}}{\partial t} The Attempt at a Solution Choose any point inside...
  38. A

    How Does Faraday’s Law Determine Induced Current in a Circuit?

    Homework Statement Given a constant magnetic field, B, into the plane of the board, how much induced current flows through R and C. Homework Equations Induced EMF =-d/dt (Fluxb) Iind= Induced EMF/R V= dx/dt = constant (velocity of sliding conductor) Lenz Law The Attempt at a Solution
  39. X

    Conceptual question about Faraday's Law

    Homework Statement A solenoid has 10 turns/cm and carries a 4-A current. A circular loop with 5 turns of area i cm^2 lies within the solenoid with its axis at 37 degrees to the axis of the solenoid. Find the magnitude of the average induced emf if the current increases by 25% in .1 seconds...
  40. L

    How Does Faraday's Law Apply to a Solenoid with an Oscillating Current?

    Homework Statement A long solenoid with 1000 turns per meter and a radius 2.00 cm carries an oscillating current given by I = (5.00A) sin (100 pi t). What is the electric field induced at a radius r = 1.00 cm.from the axis of the solenoid? What is the direction of the electric field when the...
  41. M

    Faraday's Law: False Claim & Feynman's Critique

    The version of Faraday's Law which purports to include both motional EMF and transformer EMF for circuits is false. There is no theoretical basis for it. Richard Feynman, in his "Lectures on Physics," pointed out the fact that this so-called law, what he called the "flux rule," does not always...
  42. I

    Faraday's law and uniform magnetic field

    Hello Say there's a uniform magnetic field changing in time (B=Asin(t) or something), and a ring (pic 1). so obviously by faraday's law there would be current running through the ring caused by the induced emf. Now, say we connect 2 wires from the center of the ring up to the top and to the...
  43. R

    Faraday's Law and a metal loop

    Homework Statement A metal loop is attached to an axle with a handle as shown. The north pole of a magnet is placed blow the loop and handle turned so that the looks rotates counterclockwise at a constant angular speed. Suppose the loop (the one above) were replaced by a second loop that...
  44. A

    Faraday's Law, Magnetic Flux, and the dot product

    Homework Statement We are studying Electromagnetic Induction right now. I understand the concepts, Faraday's Law and magnetic flux. But I don't understand what my book is doing. Homework Equations Magnetic Flux \phi=\intB∙dA Faraday's Law Emf = - d\phi/dt Emf=Electromotive force \phi=Magnetic...
  45. N

    A curious question on the inapplicability of Faraday's law

    I recently came across this article on wikipedia : http://en.wikipedia.org/wiki/Faraday_paradox#Inapplicability_of_Faraday.27s_law" I don't understand why is it that Faraday's law is inapplicable here. But wouldn't there be a increase in magnetic flux, since the open surface will increase in...
  46. K

    Faraday's Law problem involving selenoid.

    Homework Statement Professor K brings a 75-turn coil of radius 35mm into class for a demonstration of Faraday's Law. He applies a spatially uniform magnetic field parallel to the axis of the coil with a magnet. By moving the magnet closer to the coil, he increases the magnitude of the field at...
  47. A

    Electromagnetic waves, Faraday's law

    Homework Statement Homework Equations For a plane polarized electromagnetic wave traveling along the z axis, with its E vector parallel to the x-axis and its H vector parallel to the y axis, Faraday's law \nabla\times \textbf{E}=-\frac{\partial \textbf{B}}{\partial t} gives that...
  48. K

    Does Faraday's Law Account for Varying Induced Flux in a Loop?

    Faraday's law says induced emf = - d(flux)/dt If this is applied to a loop where induced emf causes currents, and thus flux itself, do we have to consider that flux (of course we don't if it's constant)? If the external flux has a nonzero second derivative, then the induced emf is...
  49. L

    Why Is Faraday's Law not wrong?

    ok so Faraday's Law says that \oint_C \vec{E} \cdot \vec{dr} = -\frac{\partial}{\partial t} \int_S \vec{B} \cdot \vec{dA} but we know that \vec{E}=-\nabla \varphi and so \oint_C \vec{E} \cdot \vec{dr} =-\oint_C \nabla \times \nabla \varphi \cdot \vec{dA}=0 by Stokes' Theorem...
  50. M

    Does Distance Affect the EMF According to Faraday's Law?

    This is just a general question, no calculations or homework-like wording involved! It's just a little something that has been bugging me. Faraday's law states emf = change in flux with respect to time. Let's say I'm generating this change in flux with an inductor somewhere in space. (I want...
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