# What is Faraday's law of induction: Definition and 15 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. ### Magnetic energy density, self-inductance of coaxial cylindrical shells

For ##a<r<b## we can calculate the magnetic field at some radius ##r## with Ampere's law $$\oint_C\vec{B}\cdot d\vec{l}=\mu_0 I_{enc}=\mu_0 I$$ $$\implies B=\frac{\mu_0 I}{2\pi r}$$ $$\vec{B}=\frac{\mu_0 I}{2\pi r}\hat{\theta}$$ At this point my questions arise. I don't see a current loop...
2. ### I Which law defines the AC inducing voltage in the inductor?

If we connect an inductor without ohmic resistance to the alternating voltage source, voltage should induce in the inductor because of the Faraday's law. Voltage is induced by changing magnetic flux through the inductor which is accomplished by alternating current through it. Therefore, in order...
3. ### Using Faraday's laws to find the induced EMF

Here is the question: We know the equation \epsilon = \frac{d\phi }{dt} = BAcos(\theta ). This means that the only way we can create an induced voltage is if we change the magnetic field, change the area of the loop in the magnetic field, or change the angle between the normal vector to the...
4. ### 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...

Imagine a magnet moving up and down so that its flux 'B' cuts the copper rod to produce an alternating emf, suppose if the movement is fast enough such that its frequency equals to the electron spin resonance frequency given by F = B x 2.8 Mhz per gauss, neglecting skin effect, more copper...
6. ### B Are silicon iron sheets really necessary for a commercial transformer?

Hi, everyone. I just finished studying the principle on which a transformer works. It relies on Faraday's law of induction. And my high school physics book uses the following picture for illustration: Roughly speaking, the...
7. ### About changes in a magnetic field

Here i tried this way (see picture) Please tell me am i right or wrong. Also they says find the change in magnetic field with time using Faraday's law in a rectangular loop. How can i solve that??
8. ### How is there not an infinite regress in the EMF of a motor?

Say we have a coil connected to a battery in a uniform magnetic field, perpendicular to the magnetic moment of the coil. This is a simple motor. There is a torque on the coil that varies with the angle θ between the field and the moment. Clearly, the angular velocity ω is not constant. Here is...
9. ### 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.
10. ### 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...
11. ### 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...
12. ### Can a Strong Magnet Induce EMF in a Copper Wire Solenoid from a Distance?

Is it necessary to pass magnet through solenoid in Faraday's law experiment. If not, then how much emf could be induced if a normal bar magnet crosses a copper wire solenoid from a distance of approx 1 meter.
13. ### Back emf in a single loop of wire?

I have been thinking about coils of wire carrying alternatingcurrent. From what I understand, a back emf is induced in the coil because there is a changing magnetic field around each individual loop of wire, and therefore there is a changing flux through each loop because the changing field...
14. ### Do back force and back emf come together?

i have heard it said that back force occurs in generators and back emf occurs in motors, however I was considering a motor and I thought that it seems to me that as the coil is rotating and it has the changing flux linkage, and thus a back end is induced in it by Lenz's law, this reduces the...
15. ### Two parallel wires carrying currents in the same direction.

Homework Statement Two parallel wires both carry currents directed from left to right. A circular wire loop lies in the plane of the two wires midway between them. The currents are positive charges. Sketch the changes in the magnetic fields induced and the resultant current direction in the...