🎉 The Study-to-Win Winning Ticket number has been announced! Go to your Tickets dashboard to see if you won! 🎉View Winning Ticket

Indian Institute of Technology Kharagpur

Problem 1
Problem 2
Problem 3
Problem 4
Problem 5
Problem 6
Problem 7
Problem 8
Problem 9
Problem 10
Problem 11
Problem 12
Problem 13
Problem 14
Problem 15
Problem 16
Problem 17
Problem 18
Problem 19
Problem 20
Problem 21
Problem 22
Problem 23
Problem 24
Problem 25
Problem 26
Problem 27
Problem 28
Problem 29
Problem 30
Problem 31
Problem 32
Problem 33
Problem 34
Problem 35
Problem 36
Problem 37
Problem 38
Problem 39
Problem 40
Problem 41
Problem 42
Problem 43
Problem 44
Problem 45
Problem 46
Problem 47
Problem 48
Problem 49
Problem 50
Problem 51
Problem 52
Problem 53
Problem 54
Problem 55
Problem 56
Problem 57
Problem 58
Problem 59
Problem 60
Problem 61
Problem 62
Problem 63
Problem 64
Problem 65
Problem 66
Problem 67
Problem 68
Problem 69
Problem 70
Problem 71
Problem 72
Problem 73

Problem 17

The magnetic flux through three different coils is changing as shown in Figure $P 18.17$ . For each situation, draw a corresponding graph showing qualitatively how the induced emf changes with time

Answer

For the first graph flux has a functional form $\Phi=-\Phi_{0}+c t,$ where $c$ is a positive constant. For the second graph, it would be $\Phi=\Phi_{0}-c t^{2}$ . The graphs for the induced emf versus time for each situation are sown in the below figure.

You must be logged in to bookmark a video.

...and 1,000,000 more!

OR

Join 5 million HS and College students

## Discussion

## Video Transcript

so the flat sources time graph is given So forest we will try to find defy DT With respect to time on, we can see that this is ah straight line. The functional form is phi equals negative Fine art. Thus some constant times t So if you differentiate it, then you will get a straight line and see And that we just make some space over here. We're trying to find the PMF induced, which is negative. Leafy DT. So this will be a straight line at a value off negative some constant on thesis is my part A Let's do part, B. Now this looks something like this and it looks like a parabola and the functional form can be recognized. FYI, eat grows she not. This is my feet. Not in the y axis. This is my firaxis minus C. He squared. So if I differentiate this function over here, I get dif e d t equals negative two c t. So this is a shred line with a negative slope which will look like something like this At Peak was Zito. I start from zero. No. Yeah. Man equals this and the slope is given by do you see over here? Part C part C. It will be difficult to write fee in ah functional form. However, I can see that this is a symmetry. Cars about the time axes that's going this up a little bit. That is my time axis. Well, we're here. Fox is constant. Then it linearly comes down and then it becomes costing again. That's a negative value. So once again, I'm going to find defeated ET, which is so over here you should understand that there is one section up to here where flux is not changing. So until that I have got my genuine starts to be zero from here onwards, once again, I have got my changing stuff to be zero. This will most likely be done better with covered graph. So this just draw the time axis to start wheat on and up until this section, I will have by changing starts to be zero. From here on the wars, I will have checking stops to be zero de fi dd Ah, he's the delivery of this lie which will have some negative value over here and now. My electro motive force will come out of the here, here and here for all these cases. What I have done these I am used the formula where equals negative. Do you fee DT?

## Recommended Questions

The magnetic flux through three different coils is changing as shown in Figure $P 18.18$ . For each situation, draw a corresponding graph showing quantitatively how the induced emf changes with time.

A magnetic field passes through a stationary wire loop, and its magnitude changes in time according to the graph in the drawing. The direction of the field remains constant, however. There are three equal time intervals indicated in the graph: $0-3.0 \mathrm{s}, 3.0-6.0 \mathrm{s},$ and $6.0-9.0 \mathrm{s}$ . The loop consists of 50 turns of wire and has an area of 0.15 $\mathrm{m}^{2}$ . The magnetic field is oriented parallel to the normal to the loop. For purposes of this problem, this means that $\phi=0^{\circ}$ in Equation $22.2 . \quad(\text { a ) For each }$ interval, determine the induced emf. (b) The wire has a resistance of 0.50$\Omega$ . Determine the induced current for the first and third intervals.

The accompanying figure shows a conducting ring at various positions as it moves through a magnetic field. What is the sense of the induced emf for each of those positions?

A flat coil is oriented with the plane of its area at right angles to a spatially uniform magnetic field.

The magnitude of this field varies with time according to the graph in Fig. $\mathrm{P} 29.52$ . Sketch a qualitative (but accurate!) graph of the emf induced in the coil as a function of time. Be sure to identify the times $t_{1}$ $t_{2},$ and $t_{3}$ on your graph.

In Figure P19.3, assume in each case the velocity vector shown is replaced with a wire carrying a current in the direction of the velocity vector. For each case, find the direction of the magnetic field that will produce the magnetic force shown.

Figure $P 31.47$ is a graph of the induced emf versus time for a coil of $N$ turns rotating with angular speed $\omega$ in a uniform magnetic field directed perpendicular to the coil's axis of rotation. What If? Copy this sketch (on a larger scale) and on the same set of axes show the graph of emf versus $t$ (a) if the number of turns in the coil is doubled, (b) if instead the angular speed is doubled, and (c) if the angular speed is doubled while the number of turns in the coil is halved.

A wire loop is placed in a magnetic field that is perpendicular to its plane. The field varies with time as shown in FIGURE 23-34. Rank the six regions of time in order of increasing magnitude of the induced emf. Indicate ties where appropriate.

In Figure P19.2, assume in each case the velocity vector shown is replaced with a wire carrying a current in the direction of the velocity vector. For each case, find the direction of the magnetic force acting on the wire.

Figure $\mathrm{P} 31.47$ is a graph of the induced emf versus time for a coil of $N$ turns rotating with angular speed $\omega$ in a uniform magnetic field directed perpendicular to the axis of rotation of the coil. What If? Copy this sketch (on a larger scale), and on the same set of axes show the graph of emf versus $l$ (a) if the number of turns in the coil is doubled; (b) if instead the angular speed is doubled; and (c) if the angular speed is doubled while the number of turns in the coil is halved.

MIXED REVIEW

In the four figures in item $35,$ assume that in each case the velocity vector shown is replaced with a wire carrying a current in the direction of the velocity vector. Find the direction of the magnetic force acting on each wire.