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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 9b
Chapter 29, Problem 9b

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.

Verified step by step guidance
1
Understand that the problem involves electromagnetic induction, where a changing magnetic flux through a loop induces an electromotive force (EMF) and hence a current.
The loop's circumference is decreasing, which means its area is decreasing. Since the magnetic field is constant and perpendicular to the loop, the magnetic flux through the loop is decreasing.
According to Lenz's Law, the induced current will flow in a direction that opposes the change in magnetic flux. Since the flux is decreasing, the induced current will try to increase the flux.
The magnetic field is directed into the page (as indicated by the image with crosses), so the induced current must create a magnetic field in the same direction to oppose the decrease.
Using the right-hand rule, curl your fingers in the direction of the induced current such that your thumb points in the direction of the magnetic field (into the page). The fingers will curl clockwise, indicating the direction of the induced current is clockwise when viewed along the direction of the magnetic field.

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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 Induction

Faraday's Law states that a change in magnetic flux through a loop induces an electromotive force (EMF) in the loop. The EMF is proportional to the rate of change of the magnetic flux. In this scenario, as the loop shrinks, the area decreases, leading to a change in magnetic flux, thus inducing a current.
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Faraday's Law

Lenz's Law

Lenz's Law provides the direction of the induced current, stating that the induced current will flow in a direction that opposes the change in magnetic flux. As the loop shrinks, the magnetic flux decreases, so the induced current will flow to create a magnetic field that opposes this decrease, maintaining the original flux.
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Lenz's Law

Right-Hand Rule

The Right-Hand Rule helps determine the direction of the induced current. When the thumb points in the direction of the magnetic field, the fingers curl in the direction of the induced current. In this case, looking along the direction of the magnetic field, the induced current will be counterclockwise to oppose the decrease in flux.
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Related Practice
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

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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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

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?

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Textbook Question

The armature of a small generator consists of a flat, square coil with 120 turns and sides with a length of 1.60 cm. The coil rotates in a magnetic field of 0.0750 T. What is the angular speed of the coil if the maximum emf produced is 24.0 mV?

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Textbook Question

A flat, rectangular coil of dimensions l and w is pulled with uniform speed v through a uniform magnetic field B with the plane of its area perpendicular to the field (Fig. E29.14). (a) Find the emf induced in this coil. (b) If the speed and magnetic field are both tripled, what is the induced emf?

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