IP The magnetic flux through a single-loop coil is given by...

IP The magnetic flux through a single-loop coil is given by Figure $23-27$ (a) Is the magnetic flux at $t=0.25$ s greater than, less than, or the same as the magnetic flux at $t=0.55 \mathrm{s}$ ? $\mathrm{Ex}$ plain. (b) Is the induced emf at $t=0.25$ s greater than, less than, or the same as the induced emf at $t=0.55$ s? Explain. (c) Calculate the induced emf at the times $t=0.25 \mathrm{s}$ and $t=0.55 \mathrm{s}.$

Key Concepts

Induced Electromotive Force (emf)

The induced electromotive force is the voltage generated in a circuit due to a changing magnetic flux. It is directly related to the speed at which the magnetic field changes with respect to the loop, and its magnitude can be computed using Faraday’s Law. This concept is fundamental to the operation of devices like generators and transformers.

Faraday’s Law of Electromagnetic Induction

Faraday's Law describes how a change in magnetic flux through a circuit induces an electromotive force (emf) in that circuit. It quantitatively relates the induced emf to the negative rate of change of the magnetic flux, emphasizing the dynamic relationship between magnetic fields and electrical currents in physical systems.

Magnetic Flux

Magnetic flux is a measure of the total magnetic field passing through a given surface. It is determined by the dot product of the magnetic field and the area vector over that surface, and it plays a crucial role in electromagnetism since its changes over time are responsible for the generation of electric currents in conductive loops.

Transcript

00:01 Hi, in the given problem, the variation of magnetic flux linked with a coil with the passage of time is given as here.

00:14 The time is represented, the variation of time is being represented on the x -axis and that is measured in seconds.

00:23 And the variation in flux is represented on y -axis and that is being measured in weber.

00:32 First of all, magnetic flux varies linearly, increases linearly from 0 to 10 weber in a short duration of time of 0 .1 second.

00:49 Then it remains constant up to a duration of time 0 .2 second.

00:57 Then suddenly it falls.

01:00 It falls sharply.

01:01 And at a duration of time, 0 .6 seconds, it becomes minus 5 vapor.

01:14 So the variation from 0 .2 second to 0 .6 seconds is something like this.

01:22 Here, this is 0 .5 seconds.

01:27 So this is the variation of the magnetic flux with the time given in the problem.

01:32 Now, in the first part of the problem, we have to find the magnitude of magnetic flux at a time 0 .25 second and a time 0 .55 second.

01:50 At these two times, we have to compare the magnetic flux that at which of the time the magnetic flux is more or less or same in magnitude.

02:01 So this 0 .25 second is almost here at this point.

02:07 So the flux, so the magnetic flux at 0 .25 second will be this quite large value and 0 .55 second will be almost here.

02:22 So the magnetic flux at 0 .55 second will be this.

02:26 So obviously it is clear comparing the flux, magnetic flux at these two times that the magnetic flux is greater at 0 .25 second as compared with that at 0 .55 seconds.

02:42 So comparing the magnetic flux at these two times, with the help of given curve, we conclude that the flux is more at 0 .0 .2...

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