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Ch 29: Electromagnetic Induction
Young & Freedman Calc - University Physics 14th Edition
Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610Not the one you use?Change textbook
All textbooksYoung & Freedman Calc 14th EditionCh 29: Electromagnetic InductionProblem 2b
Chapter 29, Problem 2b

In a physics laboratory experiment, a coil with 200 turns enclosing an area of 12 cm2 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. What is the average emf induced in the coil?

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First, understand that the problem involves electromagnetic induction, where a change in magnetic flux through a coil induces an electromotive force (emf). The relevant formula is Faraday's law of induction: \( \text{emf} = -N \frac{\Delta \Phi}{\Delta t} \), where \( N \) is the number of turns, \( \Delta \Phi \) is the change in magnetic flux, and \( \Delta t \) is the time interval.
Calculate the initial magnetic flux (\( \Phi_i \)) when the coil's plane is perpendicular to the magnetic field. The formula for magnetic flux is \( \Phi = B \cdot A \cdot \cos(\theta) \), where \( B \) is the magnetic field strength, \( A \) is the area, and \( \theta \) is the angle between the field and the normal to the coil. Initially, \( \theta = 0 \degree \), so \( \cos(\theta) = 1 \).
Calculate the final magnetic flux (\( \Phi_f \)) when the coil's plane is parallel to the magnetic field. In this position, \( \theta = 90 \degree \), so \( \cos(\theta) = 0 \), making the final flux \( \Phi_f = 0 \).
Determine the change in magnetic flux (\( \Delta \Phi \)) using \( \Delta \Phi = \Phi_f - \Phi_i \). Substitute the values from the previous steps to find \( \Delta \Phi \).
Substitute the values of \( N = 200 \), \( \Delta \Phi \), and \( \Delta t = 0.040 \) s into Faraday's law to calculate the average induced emf: \( \text{emf} = -N \frac{\Delta \Phi}{\Delta t} \). Remember that the negative sign indicates the direction of the induced emf according to Lenz's law, but for magnitude, you can ignore the negative sign.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Faraday's Law of Electromagnetic Induction

Faraday's Law states that a change in magnetic flux through a coil induces an electromotive force (emf) in the coil. The induced emf is proportional to the rate of change of the magnetic flux. In this experiment, the coil's rotation changes the magnetic flux, leading to an induced emf.
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Magnetic Flux

Magnetic flux is the measure of the magnetic field passing through a given area. It is calculated as the product of the magnetic field strength, the area it penetrates, and the cosine of the angle between the field and the normal to the surface. The change in orientation of the coil affects the magnetic flux, crucial for calculating the induced emf.
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Average Induced EMF

The average induced emf can be calculated using the formula: emf = -ΔΦ/Δt, where ΔΦ is the change in magnetic flux and Δt is the time interval over which the change occurs. This concept helps determine the magnitude of the emf generated during the coil's rotation in the magnetic field.
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Related Practice
Textbook Question

A single loop of wire with an area of 0.0900 m2 is in a uniform magnetic field that has an initial value of 3.80 T, is perpendicular to the plane of the loop, and is decreasing at a constant rate of 0.190 T/s. What emf is induced in this loop?

Textbook Question

In a physics laboratory experiment, a coil with 200 turns enclosing an area of 12 cm2 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. What is the total magnetic flux through the coil before it is rotated? After it is rotated?

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Textbook Question

Shrinking Loop. A circular loop of flexible iron wire has an initial circumference of 165.0 cm, but its circumference is decreasing at a constant rate of 12.0 cm/s due to a tangential pull on the wire. The loop is in a constant, uniform magnetic field oriented perpendicular to the plane of the loop and with magnitude 0.500 T. Find the emf induced in the loop at the instant when 9.0 s have passed.

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Textbook Question

Shrinking Loop. A circular loop of flexible iron wire has an initial circumference of 165.0 cm, but its circumference is decreasing at a constant rate of 12.0 cm/s due to a tangential pull on the wire. The loop is in a constant, uniform magnetic field oriented perpendicular to the plane of the loop and with magnitude 0.500 T. Find the direction of the induced current in the loop as viewed looking along the direction of the magnetic field.

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Textbook Question

A closely wound rectangular coil of 80 turns has dimen-sions of 25.0 cm by 40.0 cm. The plane of the coil is rotated from a position where it makes an angle of 37.0° with a magnetic field of 1.70 T to a position perpendicular to the field. The rotation takes 0.0600 s. What is the average emf induced in the coil?

Textbook Question

A single loop of wire with an area of 0.0900 m2 is in a uniform magnetic field that has an initial value of 3.80 T, is perpendicular to the plane of the loop, and is decreasing at a constant rate of 0.190 T/s. If the loop has a resistance of 0.600 Ω, find the current induced in the loop.

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