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Ch 29: Electromagnetic Induction

Chapter 29, Problem 29

In a physics laboratory experiment, a coil with 200 turns enclosing an area of 12 cm^2 is rotated in 0.040 s from a position where its plane is perpendicular to the earth's magnetic field to a position where its plane is parallel to the field. The earth's magnetic field at the lab location is 6.0*10-5 T. (a) What is the total magnetic flux through the coil before it is rotated? After it is rotated?

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Hey, everyone. So this problem is dealing with magnetic flux. Let's see what it's asking us. We have the axis of a circular coil that is rotated from 30 degrees to 70 degrees in 700.5 seconds. And that's in respect or with respect to the earth's magnetic field, the cross sectional area of the coil is 16 centimeters squared and the number of turns is 300. We're given earth's magnetic field value which is seven times 10 to the negative five teslas. And then we're asked to calculate the total magnetic flux through the coil initially when it's at degrees. And finally, when it's at 70 degrees, our answers will have both an initial and a final flux. And they are a 1.15 times 10 to the negative five and 2.12 point 91 times 10 to the negative five Wevers B 1.91 times 10 to the negative five and 2. times 10 to the negative five Wevers C 9.7 times 10 to the negative five and eight point sorry. And 3.83 times 10 to the negative five Wevers or D 2.91 times 10 to the negative five and 1.15 times 10 to the negative five letters. OK. So the first thing that we can recall here is that the magnetic flux through each turn is given by the equation Bye B which is paramagnetic flux is equal to B, the magnitude of our magnetic field multiplied by a cross sectional area multiplied by the cosine of data. And so we have B given to us in the problem, our cross sectional area was also given to us. And then our theta initially, we're going to have um degrees angle and then our final angle is going to be 70 degrees. And then our total flux is simply going to be N the number of terms multiplied by the flux through each term NBA go sign data. So initially, we have and no, I'm um magnitude of our magnetic field was given at seven times 10 to the negative five teslas multiplied it by our cross sectional area. And so that was given in the problem as 16 centimeter squared, we need to keep everything in standard units. So that's going to be 10, 16 times 10 to the negative four m squared multiplied by cosine of and sorry, we know N and N is 300. And so we can just plug all of that in and get our initial block and that is 2.91 times 10 to the negative five S. And we're going to do the same thing for our final total flux, the same equation. So it's going to be 300 turns seven times 10 to the negative fifth teslas multiplied by 16 times 10 to the negative four m squared. And now this time is cosine of the final beta which is 70 degrees. And so when we plug that in, we get a total final flux of 1.15 times 10 to the negative five letters. And so that is those two, I should say are the answer to this problem. We go back up to our multiple choice solutions. It aligns with answer choice D. So that's all we have for this one. We'll see you in the next video.
Related Practice
Textbook Question
The current in Fig. E29.18 obeys the equation I(t) = I_0e^(-bt), where b > 0.

Find the direction (clockwise or counterclockwise) of the current induced in the round coil for t > 0.
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Textbook Question
A circular loop of wire with radius r = 0.0480 m and resistance R = 0.160 Ω is in a region of spatially uniform magnetic field, as shown in Fig. E29.22. The magnetic field is directed out of the plane of the figure. The magnetic field has an initial value of 8.00 T and is decreasing at a rate of dB/dt = -0.680 T/s.

(a) Is the induced current in the loop clockwise or counterclockwise?
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Textbook Question
In a physics laboratory experiment, a coil with 200 turns enclosing an area of 12 cm^2 is rotated in 0.040 s from a position where its plane is perpendicular to the earth's magnetic field to a position where its plane is parallel to the field. The earth's magnetic field at the lab location is 6.0*10-5 T. (b) What is the average emf induced in the coil?
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Textbook Question
Using Lenz's law, determine the direction of the current in resistor ab of Fig. E29.19 when (a) switch S is opened after having been closed for several minutes; (b) coil B is brought closer to coil A with the switch closed; (c) the resistance of R is decreased while the switch remains closed.
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Textbook Question
A cardboard tube is wrapped with two windings of insulated wire wound in opposite directions, as shown in Fig. E29.20. Terminals a and bof winding A may be connected to a battery through a revers-ing switch. State whether the induced current in the resistor Ris from left to right or from right to left in the following circumstances: (a) the current in winding Ais from a to b and is increasing; (b) the current in winding A is from b to a and is decreasing; (c) the current in winding A is from b to a and is increasing.
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Textbook Question
A Step-Down Transformer. A transformer connected to a 120-V (rms) ac line is to supply 12.0 V (rms) to a portable electronic device. The load resistance in the secondary is 5.00 Ω. (a) What should the ratio of primary to secondary turns of the transformer be?
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