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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
Chapter 29, Problem 1b

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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1
Start by understanding Faraday's Law of Induction, which states that the induced electromotive force (EMF) in a closed loop is equal to the negative rate of change of magnetic flux through the loop. The formula is: ε = -Φ>t>.
Calculate the change in magnetic flux, Φ, using the formula: Φ = B A, where B is the magnetic field and A is the area of the loop. Since the magnetic field is decreasing, the rate of change of the magnetic field is given as -0.190 T/s.
Substitute the values into the formula for EMF: ε = -A B>t>. Here, A = 0.0900 m2 and B>t> = -0.190 T/s.
Use Ohm's Law to find the induced current, I, in the loop. Ohm's Law states that I = εR, where R is the resistance of the loop, given as 0.600 Ω.
Substitute the calculated EMF into Ohm's Law to find the current: I = ε0.600. This will give you the magnitude of the induced current in the loop.

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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 loop induces an electromotive force (EMF) in the wire. The induced EMF is proportional to the rate of change of the magnetic flux. In this scenario, the decreasing magnetic field causes a change in flux, leading to an induced EMF in the loop.
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Faraday's Law

Magnetic Flux

Magnetic flux is the product of the magnetic field strength and the area it penetrates, perpendicular to the field lines. It quantifies the total magnetic field passing through a surface. Here, the flux changes due to the decreasing magnetic field, which is crucial for calculating the induced EMF using Faraday's Law.
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Ohm's Law

Ohm's Law relates the current flowing through a conductor to the voltage across it and its resistance, expressed as I = V/R. In this problem, the induced EMF acts as the voltage, and the loop's resistance is given, allowing us to calculate the induced current using this fundamental principle.
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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?

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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 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

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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