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30. Induction and Inductance
Lenz's Law
Problem 19
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.


1
Step 1: Understand Lenz's Law, which states that the direction of the induced current in a circuit is such that it opposes the change in magnetic flux that produced it. This is a consequence of the conservation of energy.
Step 2: For part (a), when switch S is opened after being closed for several minutes, the current in coil A stops, reducing the magnetic field through coil B. According to Lenz's Law, coil B will induce a current to oppose this decrease in magnetic flux. Determine the direction of this induced current by considering the direction of the original magnetic field and the direction needed to oppose its reduction.
Step 3: For part (b), when coil B is brought closer to coil A with the switch closed, the magnetic flux through coil B increases. Lenz's Law dictates that the induced current in coil B will oppose this increase in magnetic flux. Analyze the direction of the original magnetic field and the direction needed to oppose its increase to find the direction of the induced current.
Step 4: For part (c), when the resistance of R is decreased while the switch remains closed, the current in coil A increases, thereby increasing the magnetic field through coil B. Lenz's Law states that the induced current in coil B will oppose this increase in magnetic flux. Determine the direction of the original magnetic field and the direction needed to oppose its increase to find the direction of the induced current.
Step 5: In each scenario, use the right-hand rule to determine the direction of the induced current. Point your thumb in the direction of the magnetic field and curl your fingers; the direction your fingers curl is the direction of the induced current that opposes the change in magnetic flux.

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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Lenz's Law
Lenz's Law states that the direction of the induced current in a closed loop is such that it opposes the change in magnetic flux that produced it. This is a consequence of the conservation of energy and is mathematically represented by a negative sign in Faraday's law of electromagnetic induction. It helps determine the direction of induced currents in scenarios involving changing magnetic fields.
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Electromagnetic Induction
Electromagnetic induction is the process by which a changing magnetic field within a closed loop induces an electromotive force (EMF) and consequently an electric current in the loop. This phenomenon is described by Faraday's law, which states that the induced EMF is proportional to the rate of change of magnetic flux through the loop. Understanding this concept is crucial for analyzing how currents are induced in circuits.
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Introduction to Induction
Magnetic Flux
Magnetic flux refers to the total magnetic field passing through a given area, typically measured in webers (Wb). 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. Changes in magnetic flux are central to the process of electromagnetic induction, as they determine the magnitude and direction of induced currents.
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Related Practice
Multiple Choice
In a region of space, a magnetic field is increasing at . A square loop of wire with a side of is oriented perpendicular to the field. The loop has a total resistance of . What current is induced in the loop?
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