# Faraday law Definition and 17 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. ### Induced Electrical Field (Maxwell-Faraday's Law)

As we know that the magnetic induction causes an electric current in a wire and Faraday has formulated his Electromotive equation ##\epsilon=-\frac{d\Phi}{dt}##. And then Maxwell-Faraday's equation is: ##\nabla \times E=-\frac{\partial B}{\partial t}##, until now this was just an introduction...
2. ### 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...
3. ### Finding the induced EMF in a solenoid-wire system

I know that ##B = \mu n I## and ##\phi = B \pi R^2##. So with have ##d\phi / dt = \mu n \alpha \pi R^2##. But I don't know what to do with this? is this the answer? I don't think so but I don't know what to do after this.
4. ### Conductive loop that is contracting in a magnetic field

$$V = \int \left(\vec{v} \times \vec{B}\right) \bullet \vec{dl} - \int _S \frac{\vec{dB}}{dt} \bullet \vec{ds}$$ From the statement I know that: B⊥v, (B x v) // dl and B // ds. $$V = \int vBdl - \oint _S \frac{dB}{dt} ds$$ v is the speed with which all the segments dl are aproximating to the...
5. ### Direction of current in smaller loop on the left and on the right

Lets say the current in the larger loop is counterclockwise. Then it doesn't matter if the smaller loop is to the right or to the left of the larger one, the induced current in it will always be clockwise. The magnetic field due to the smaller loop current always points in the negative...
6. ### Loop falling in a magnetic field

(a) Let's say the loop has fallen ##y## from its initial position. Then the magnetic flux is ##B_{0}w(h-y)## and the induced voltage is ##\mathcal{E}=B_{0}wdy/dt##. Since this voltage is positive, the current flows clockwise. (b) ##I=\frac{\mathcal{E}}{R}=\frac{B_{0}wv}{R}## (c) The force on...
7. ### B Induced EMF in an Open Loop

Let's say you have an open loop (like a section of a circle) in a changing magnetic field. I think there would be an induced EMF, but no current. What I can't figure out, though, is how to calculate the induced EMF. Using Faraday's law doesn't seem to help, as there's no enclosed area.
8. ### Sign of the Faraday-Lenz equation

Homework Statement Hello, good afternoon, I have a question that's coming up when I'm doing electromagnetic induction exercises. In some exercises they ask me to determine the electromotive force (iee), and when they do the exercise resolution they do it with absolute value. In other...
9. ### Classical Book(s) with problems on classical electromagnetism

I started studying the book "A Student's Guide to Maxwell's Equations" by Daniel Fleisch some time back. It is an excellent book, giving a very good idea about the main laws of electromagnetism. I will soon finish the book. Now I need some book(s) which has problems on all the laws in classical...
10. ### Time-dependent potential difference between two ends of a loop

Homework Statement A straight copper wire that carries a sinusoidal current with an alternating frequency of 50 Hz and a maximum amplitude of 0.5 A passes through the centre of a circular ring of a second copper wire, with the two wires orientated perpendicularly to each other. The radius of...
11. ### Rotating disc in a rotating magnetic field

Homework Statement :A metallic disc of radius R is placed perpendicular to a magnetic field B.Both the magnetic field and the disc rotate with an angular velocity w about the axis of the disc.Find the induced EMF between the center and the circumference[/B] Homework Equations Motional...
12. ### 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...
13. ### Theory in approaching Faraday law/circuit question

Homework Statement I have a square conducting loop of size L that contains two identical lightbulbs 1 and 2. The magnetic field that goes into the page varies B(t) = a*t + b. Lightbulbs have resistance of R0 Here is a question and the sample response. Disregard the part of the question that...
14. ### Magnetic induction/ goal ref technology

Hi, I am interested in the basics of "goal ref technology", but I was not able to find a lot of material. Just one very brief wikipedia page and some paragraphs at the http://www.iis.fraunhofer.de/en/ff/kom/proj/goalref.html#. Does this work a bit like the anti shoplifting RFID tags? As far...
15. ### I Strange Magnus Force in a Whirlpool

1. Imagine a big river with water flowing constant velocity , assume there is a whirlpool at center as shown in the figure. 2. Because of the magnus force the whirlpool should move towards left or right towards river bank depending on the spin, but it does't happens it just stays fine in its...
16. ### B-field generated by inducting loop of shrinking size (NEED SOMEONE TO CHECK ANSWERS)

Homework Statement A little stuck on the second question it basically boils down to not quite understanding the question. Was hoping someone here could push me in the right direction. The Question is two part, already completed the first half but wouldn't mind if someone looked over it while...
17. ### Magnetic Levitation : Confusion with Lenz's Law

Considering the above diagram, I am failing to see why the aluminium ring floats upwards rather than oscillates. I understand Faraday's law, but I am struggling with Lenz's law - as there is an alternating current, an alternating magnetic field is produced, similar to a sine wave. Therefore, I...