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30. Induction and Inductance

Lenz's Law

Physics

30. Induction and Inductance

Lenz's Law

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2:10 minutes

Problem 7

Textbook Question

(II) If the solenoid in Fig. 29–47 is being pulled away from the loop shown, in what direction is the induced current in the loop? Explain.

Verified step by step guidance

Step 1: Understand the concept of electromagnetic induction. When the magnetic flux through a loop changes, an induced current is generated in the loop according to Faraday's Law. The direction of the induced current is determined by Lenz's Law, which states that the induced current will oppose the change in magnetic flux.

Step 2: Analyze the situation described in the problem. The solenoid is being pulled away from the loop, which means the magnetic field produced by the solenoid is decreasing in the region of the loop. This reduction in magnetic flux through the loop is the key factor causing the induced current.

Step 3: Apply Lenz's Law. Since the magnetic flux is decreasing, the induced current in the loop will act to oppose this decrease. To do so, the induced current will create its own magnetic field in the same direction as the original field produced by the solenoid.

Step 4: Determine the direction of the induced current. Use the right-hand rule to find the direction of the induced current. If the solenoid's magnetic field points into the plane of the loop, the induced current will flow in a direction that maintains this field (clockwise or counterclockwise depending on the orientation).

Step 5: Conclude the direction of the induced current. Based on the orientation of the solenoid's magnetic field and the application of Lenz's Law, the induced current in the loop will flow in the direction that opposes the decrease in magnetic flux caused by the solenoid being pulled away.

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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 circuit induces an electromotive force (EMF) in that circuit. The induced EMF is proportional to the rate of change of the magnetic flux. This principle is fundamental in understanding how moving a magnet or changing the magnetic field around a conductor can generate electric current.

Lenz's Law

Lenz's Law provides the direction of the induced current resulting from electromagnetic induction. It states that the induced current will flow in a direction that opposes the change in magnetic flux that produced it. This means that if the magnetic field through a loop is decreasing, the induced current will flow in a direction that attempts to maintain the original magnetic field.

Magnetic Flux

Magnetic flux is a measure of the quantity of magnetism, taking into account the strength and the extent of a magnetic field. It is defined as the product of the magnetic field strength and the area through which the field lines pass, and it is affected by the angle between the field lines and the surface area. Understanding magnetic flux is crucial for analyzing how changes in the magnetic environment affect induced currents in nearby conductors.

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Related Practice

Textbook Question

A solenoid is wound as shown in FIGURE EX30.9. Is there an induced current as magnet 2 is moved away from the solenoid? If so, what is the current direction through resistor R?

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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 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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Textbook Question

FIGURE P30.47 shows a 1.0-cm-diameter loop with R = 0.50 Ω inside a 2.0-cm-diameter solenoid. The solenoid is 8.0 cm long, has 120 turns, and carries the current shown in the graph. A positive current is cw when seen from the left. Determine the current in the loop at t = 0.010 s.

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Multiple Choice

An outer ring is connected to a variable voltage source. If the battery's voltage is continuously INCREASING, what is the direction of the induced current in the inner ring, centered inside of the outer ring?

What emf is created in a