# What is Faraday's law: Definition and 264 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. ### Understanding the math of definition of electromotive force

Does this mean we can write the following? $$\mathcal{E}=\oint_C \vec{E}\cdot d\vec{r}+\oint_C \vec{v}\times\vec{B}\cdot d\vec{r}\tag{3}$$ I haven't seen an equation like the above in my books and notes yet. What I have seen are two cases. In one case, we have a uniform magnetic field and we...
2. ### Making sense of sequence of ideas in MIT OCW's 8.02 notes on Faraday

Scenario 1 Consider a conducting bar of length ##l## moving through a uniform magnetic field as depicted below 1. Particles with charge ##q## inside experience a magnetic force ##\vec{F}_B=q\vec{v}\times\vec{B}## that pushes them upward, leaving negative charge on the lower end. 2. An...
3. ### Electromagnetic induction (Faraday's law)

I used the formulas above and got the right answer: ##\phi=4\pi t## ##\Phi_B=0.128\cos 4\pi t## ##\epsilon=1.61\sin 4\pi t## ##\epsilon_\text{max}=1.61\ V## But I still have a question: Faraday's law requires a closed loop, whereas the semi-circular loop I used was open on one side.
4. ### Maximum voltage in the primary circuit of a transformer

The alternating current will create an induced voltage given by ##V=-N\frac{d\phi(\vec{B})}{dt}=-N\frac{\Delta\phi(\vec{B})}{\Delta t}=N\frac{2 B_0 S}{\Delta t}=\frac{240\cdot 2\cdot 65\cdot 10^{-3}\cdot 10\cdot 10^{-4}}{10\cdot 10^{-3}}=3.12 V## and since this is the effective voltage, the...
5. ### Electron in a time variable magnetic field

TL;DR Summary: Find acceleration of electron in dB/dt >0 Hello. Here is a problem that i'm not so sure about: Inside a solenoid there is a time-dipendent magnetic field B, so we have dB/dt = b (constant). We want to know the acceleration of an electron: a) placed in the center of the solenoid...
6. ### Measuring the Speed of Sound in Water, Using Faraday's Law

Hi! This project involves both mechanical and electrical elements, so I'm discussing it in this forum since I'm not sure which one it would fit better into. I'm working on an experiment in which I'm trying to measure the speed of sound through water. The approach is simple: I have a long...
7. ### Faraday's law and Magnetic Fields

I am not really sure which direction i am moving in with this solution
8. ### Inducing Voltage in a Transformer: How Does It Work?

A changing current in a transformer primary produces a changing magnetic field, which induces a voltage in the secondary (correct?), but if no circuits are closed on the secondary, there's no current in the secondary (and therefore primary as well). So how is this voltage induced?
9. ### I Faraday's Law Equation: Derivative vs Delta

My textbook gives the equation for Faraday's Law as ε=-(dΦB)/(dt) , the derivative of magnetic flux with respect to time. I have also seen Faraday's law expressed as ε= -(ΔΦB)/(Δt). Are these two forms equivalent? Thanks!
10. ### Maximum charge on the plates of a capacitor

What I have done: The electromotive force due to Faraday's Law is: ##\mathcal{E}=-\frac{d\phi(\vec{B})}{dt}=\frac{d}{dt}(Ba^2)=a^2\frac{dB}{dt}=-10^{-4}V.## In the circuit, going around the loop in a clockwise fashion: ##\oint_{\Gamma}\vec{E}\cdot d\vec{l}=-\frac{d\phi(\vec{B})}{dt}\Rightarrow...

12. ### Why is there no negative sign in the Faraday's Law stated here

Summary:: Figure b also shows that there is no negative sign in Faraday's Law. How do I know when to include the negative sign?
13. ### Going From EMF to Faraday's Law to find E-field in my HW problem

Ok, so I understand how to find dphi/dt that is integral of -d/dt(B "dot" da). In this case I find a Phi that is a constant in space in time which causes me confusion in next step. Edit: dphi/dt is constant... Grithff's then says E field same as a Mag field above center of circular current. He...
14. ### Experimental investigation of Faraday's Law of Induction

Looking at how the induced EMF is proportional to the rate of change of magnetic flux, intuitively it seems that if I increase the velocity of the magnet through the solenoid, i.e. drop it from a higher height, the EMF should increase as well. However, I am unsure if this is true and can't seem...

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17. ### Show that Faraday's Law holds

I've calculated the negative time derivative of B(r, t) as: $$-\frac{\partial B}{\partial t} = k~\text x~E_0~\text{sin}(k \cdot r - \omega t + \phi)$$ The cross product can be easily expanded, I'd just rather not do the LaTeX for if I can avoid it. The Curl of the electric field...
18. ### Faraday's law -- How is the RHS required for all surfaces?

∫c Edl =-d/dt∫sBda
19. ### Find maximum current in a coil using oscilloscopes and Faraday's Law?

The experiment consists of a large field coil (connected to a current source) surrounding a coplanar and coaxial small detector coil in the center of the field coil connected to the oscilloscope. 1. Matching Current v. Time Graphs to Oscilloscope Graphs Example of one pair of graphs (I'll...
20. ### An Interesting Question on Faraday's Law of Electromagnetic Induction

On examining Maxwell's third equation which is about time varying magnetic fields (Faraday's electromagnetic induction) we find that time varying magnetic fields produce loops of electric fields in space irrespective of whether a coil is present or not, if any coil is present then these loops of...
21. ### Using Faraday's Law to calculate the magnetic field

I got stuck near the beginning, so I tried working backwards. Starting from B = (k X E0)/ω * cos(k⋅r - ωt +φ) I found -∂B/∂t = -k X E0 sin(k⋅r - ωt +φ) So now I need to find ∇ X (E0 cos(k⋅r - ωt +φ)) and see that it is equal to the above result. This is where I'm stuck though, I'm not sure...
22. ### What is the relationship between voltage and flux in Faraday's Law?

A former colleague asked me a simple question about Faraday's law. As shown below, the configuration is just a circular conductor and a changing B field, and then tried to measure the voltage across the diameter. But I am not sure what the answer is? Any help would be greatly appreciated.
23. ### Eddy currents in Faraday's Law Experiment

My explanation: A circular coil is connected to an AC supply at a frequency of 30-50 kHz (radio frequency). Therefore, an alternate current will be running through this “primary” coil, producing an alternating magnetic field. This magnetic field periodically decreases in strength, alternating...
24. ### Work Done by an Induced Electric Field

I have drawn a picture of what the induced electric field will look like, and I have determined its magnitude both within and outside of the magnetic field. I was able to get the right answer for part (b) with this information, but I don't understand why the answer for part (c) is 0 J. It...
25. ### Induced EMF and current for a bar sliding on a circular rail

On the left: my copy of the illustration in the problem. On the right: top view, with the angle. The problem gives the magnitude of the magnetic field, the radius of the rail, the resistance of the resistor, the initial rotational frequency of the bar. I am able to obtain the given solutions...
26. ### Solving Faraday's Law: 0.73V Induced EMF Help Needed

I have a simple sketch of the diagram, and I know I must use the vertical component of the magnetic field of the Earth when doing this problem I got an induced emf of 0.73 volts but I do not know if I correctly substituted the right values into faraday's law equation? Any help will be really...
27. ### Where Does the N in Faraday's Law of Induction Go?

Hello Lets take an example: imagine a horizontal magnetic field, then a wire of length L. I push the wire with a force F through the field perpendicularly with respect to the magn. field for a distance of dS. EMF = work/charge --> F*dS/I*dt, where F = flux density*current*lenght of conductor...
28. ### Faraday's Law & Motional EMF Confusion

Hi there! I have what I hope is a relatively straightforward question regarding Faraday's law and motional emf, but its been causing me to scratch my head for quite a while. Consider the diagram attached to this post (source is linked at the bottom). Assume that all of the wires and the rod are...
29. ### Faraday's Law and the distance from another wire

Hello, I have a conceptual question regarding Faraday's Law: emf = d/dt(Φ), where |Φ|=|B*A|. My question is does Faraday's Law take into account the distance between the solenoid producing the non-coulombic electrical field (Enc) and a wire circling the solenoid, which now have an emf due to the...
30. ### Faraday's Law - Balloon Problem

a) Calculate the proposed induced emf along the equator of the balloon. (horizontal equator), at the moment indicated above. $$V(t) = V + Ft \implies \frac{4 \pi r^3(t)}{3} = V + Ft \implies r(t) = \sqrt[3]{\frac{3V+3Ft}{4 \pi}}$$ $$\phi = B \pi r^2(t) = B\pi (\frac{3V+3Ft}{4 \pi})^{2/3}$$...
31. ### What is the Correct Approach for Solving Faraday's Law Problem?

This seems like just another Faraday's Law problem, but I'm getting the wrong answer according to the book. I think I'm only calculating the answer for the interval ωt = 0 and ωt = pi/2, when the |B→| is increasing. Basically you just calculate the magnetic flux through the area of the loop...
32. ### Appropriate Language when Discussing Faraday's Law

Quick question, when discussing induce emf, would you state: "An emf is induced in the coil..." or "An emf is induced across the coil..." The reason I ask is that grammatically, it sounds proper to state "An electromotive force is induced in..." (something). However, an emf is a potential...
33. ### Exploring the Role of the Vector Potential in Faraday's Law of Induction

Suppose there is an almost infinitly long but narrow solenoid with an AC current surrounded by a much larger loop such that there is no magnetic field except in the solenoid. I had always thought it didn't matter what part of the outer loop the flux changed in, there would be an induced electric...
34. ### Understand Faraday's Law and Lenz' Law

Above is an example figure. 2. When a ring in a changing magnetic field is not complete (i.e. open circuit with a small gap), how to analyze the emf of the ring? According to the general form of Faraday's law, ## \oint \vec{E} \cdot d \vec{s} = -\frac{d \Phi}{dt} ##, I deduce that although it...
35. ### Exploring EMF and Faraday's Law in LR Circuits

1) Take a non-steady circuit such as an LR circuit. Why does Kirchoff's voltage law work when analyzing such a circuit? Is it because we're assuming that dI/dt and thus dB/dt are approximately zero thus meaning that curl E is approximately zero? 2) ε, the electromotive force, is the line...
36. ### Conceptual difference between a motor and a generator

Hi. In order to explain the motion of an (accelerating) electromotor, we need the Lorentz force which itself is not one of Maxwell's equations. Conversely, if we use the same electromotor inversely to generate electricity, Faraday's law (which is a Maxwell's equation) and the resistance of the...
37. ### Faraday's Law with Zero Resistance Current Loop

Hi there, I was recently helping a friend of mine with a fairly standard electromagnetic induction problem (a basic sketch of the set-up is attached) where we have a current loop with resistance ##R## moving through a magnetic dipole and had to roughly sketch out the current induced in the loop...
38. ### Electromagnetic Induction and Faraday's Law w/ Right Hand Rule

Homework Statement Homework Equations Right Hand Rule The Attempt at a Solution I am not understanding why the force is left. I can only figure out that the current in the solenoid is moving clockwise because of the right hand rule. From there, I see that the induced current might be...
39. ### Maxwell Equations without Faraday's Law

Maxwell equations are composed of: Gauss's Law Gauss's Law for Magnetism Faraday's Law Ampere's law with Maxwell addition If you take out Faraday's Law.. can other laws re constitute it? Or are they independent? I want to know how the world would behave if there were no Faraday's Law. Note...
40. ### Consistency of Faraday's Law and Electric Field Equation in Optics

Homework Statement Suppose that an electric field is given by E(r,t)=E0cos(k·r−ωt+φ), where k⊥E0 and φ is a constant phase. Show that B(r,t)=((k×E)/ω)B(k⋅r-ωt+φ) is consistent with ∇×E=-∂B/∂t Homework Equations ∇×E=-∂B/∂t The Attempt at a Solution I know I have to take the curl of E, but I'm...
41. ### Potential Difference & Faraday's Law: Exploring the Relationship

The potential difference between two points is given ans the negative of integral of E(vector) <dot product> dl(vector) from initial to final points. Therefore, integral integral of E(vector) <dot product> dl(vector) from initial to final point should give the negative of potential difference...
42. ### Faraday's law and linearly time dependent B field

Homework Statement A positron is moving in a circular orbit of radius r = 2cm within a uniform magnetic field B0 = 50##\mu##T. The magnetic field varies over time according to the expression: B = 700t + Bo and, therefore, each orbit can be considered almost circular. (a) Calculate the...
43. ### Faraday's Law - loop turning in the Earth's B-field

Homework Statement Homework Equations Faraday's Law, Ohm's Law, definition of current[/B]The Attempt at a Solution We were given this solution:[/B] The above solution is leaving out a lot of intermediary steps. I don't agree that "the axis of the coil is at 20°, not 70°, from the...
44. ### How to find speed with Faraday's law

Homework Statement A metal rod can slide on a rail without any friction in the presence of uniform magnetic field of B=1T which is perpendicular to the plane of the paper.The distance between the tracks is d=0.1m and the resistance given is R=0.1 ohm.The resistance of the rail is negligible and...

46. ### Apparent ambiguity in the E field direction in Faraday's Law

I'm confused by an apparent ambiguity in the direction the E field in Faraday's law: ∫ E°dl = - ∂/∂t ∫ B°da Faraday's law says the change in magnetic flux through an open surface gives rise to an emf equal to E°dl taken around the closed loop which is the boundary of the open surface. And...
47. ### 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...
48. ### 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...
49. ### 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...
50. ### 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...