Problem 4Your textbook calls the electric generator "probably the most important technological application ofinduction." Let's consider an example of such a generator, consisting of a single round loop of wire ofR 100. The loop is rotated at a frequency f of 60 turns per second (and thus at 60 x 2T radiansper second). As shown in the figure below, the rotation axis of the loop is through its diameter andperpendicular to the page, and the loop rotates clockwise. We place the loop in a uniform magneticfield of strength B 0.50T that points to the right. Note that the loop is arranged so that itsrotation axis is perpendicular to the field. The angle 0 measures the angle between the field and thenormal onto the plane of the loop. An oscillating current with an amplitude of Io = 1.5 A is inducedPiyotВCircular loop(a) Assuming we let t 0 correspond to 0 0° (i.e., the loop is vertical), show that the flux throughthe loop as a function of time is given byФв (0) — Впr? сos(2т ft),where r is the (unknown) radius of the loop(b) Using your result from part (a), show that the magnitude of the induced emf as a function oftime is given bydФв|E =Bar2(27fsin(2Tft)dt(c) Using your result from part (b), Ohm's law, and the numerical values given in the problem, findthe radius of the loop(d) If the loop is rotated more slowly, then if we wanted to get the same induced current we wouldneed a larger loop. Explain why this is true, and check that your solution is consistent with thisprediction

Question
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Step 1

Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and specify the other subparts (up to 3) you’d like answered.

Step 2

Given:

Resistance of wire loop R = 100 Ω

Rotational frequency of the loop is f = 60 turns/s = 60×2π rad/s

Magnitude of magnetic field B = 0.50 T

Angle between rotation axis and magnetic field = θ

Induced oscillating current Io = 1.5 A

Step 3

(a)

The flux through the l...

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The text passage contains a physics problem about an electric generator, with multiple sub-questions asking to derive equations and explain concepts related to the induced current and magnetic flux in a rotating loop.
multiple_questions

the passage presents a detailed physics problem with multiple sub-parts (a, b, c, d) that ask the reader to:
- derive an equation for magnetic flux through a rotating loop
- derive an equation for induced emf 
- calculate the radius of the loop
- explain the relationship between rotation speed and loop size

while the problem is physics-focused, it does contain multiple mathematical questions that require derivations and calculations. however, the passage does not provide answers to these questions, only the problem statement and prompts.
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
Problem 4Your textbook calls the electric generator "probably the most important technological application ofinduction." Let's consider an example of such a generator, consisting of a single round loop of wire ofR 100. The loop is rotated at a frequency f of 60 turns per second (and thus at 60 x 2T radiansper second). As shown in the figure below, the rotation axis of the loop is through its diameter andperpendicular to the page, and the loop rotates clockwise. We place the loop in a uniform magneticfield of strength B 0.50T that points to the right. Note that the loop is arranged so that itsrotation axis is perpendicular to the field. The angle 0 measures the angle between the field and thenormal onto the plane of the loop. An oscillating current with an amplitude of Io = 1.5 A is inducedPiyotВCircular loop(a) Assuming we let t 0 correspond to 0 0° (i.e., the loop is vertical), show that the flux throughthe loop as a function of time is given byФв (0) — Впr? сos(2т ft),where r is the (unknown) radius of the loop(b) Using your result from part (a), show that the magnitude of the induced emf as a function oftime is given bydФв|E =Bar2(27fsin(2Tft)dt(c) Using your result from part (b), Ohm's law, and the numerical values given in the problem, findthe radius of the loop(d) If the loop is rotated more slowly, then if we wanted to get the same induced current we wouldneed a larger loop. Explain why this is true, and check that your solution is consistent with thisprediction

Question
39 views
check_circle

Step 1

Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and specify the other subparts (up to 3) you’d like answered.

Step 2

Given:

Resistance of wire loop R = 100 Ω

Rotational frequency of the loop is f = 60 turns/s = 60×2π rad/s

Magnitude of magnetic field B = 0.50 T

Angle between rotation axis and magnetic field = θ

Induced oscillating current Io = 1.5 A

Step 3

(a)

The flux through the l...

Want to see the full answer?

See Solution

Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour.*

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*Response times may vary by subject and question.
Tagged in
user
The text passage contains a physics problem about an electric generator, with multiple sub-questions asking to derive equations and explain concepts related to the induced current and magnetic flux in a rotating loop.

TYPE: MULTIPLE_QUESTIONS

The passage presents a detailed physics problem with multiple sub-parts (a, b, c, d) that ask the reader to:
- Derive an equation for magnetic flux through a rotating loop
- Derive an equation for induced emf 
- Calculate the radius of the loop
- Explain the relationship between rotation speed and loop size

While the problem is physics-focused, it does contain multiple mathematical questions that require derivations and calculations. However, the passage does not provide answers to these questions, only the problem statement and prompts.