Ch 30: Electromagnetic Induction

Knight Calc - Physics for Scientists and Engineers 5th Edition

Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Not the one you use?Change textbook

Knight Calc 5th Edition

Ch 30: Electromagnetic Induction

Problem 54a

Chapter 30, Problem 54a

CALC The L-shaped conductor in FIGURE P30.54 moves at 10 m/s across and touches a stationary L-shaped conductor in a 0.10 T magnetic field. The two vertices overlap, so that the enclosed area is zero, at t = 0 s. The conductor has a resistance of 0.010 ohms per meter. a. What is the direction of the induced current?

Verified step by step guidance

Step 1: Understand the concept of electromagnetic induction. When a conductor moves through a magnetic field, a change in the magnetic flux through the enclosed area induces an electromotive force (EMF) according to Faraday's Law of Induction. The direction of the induced current can be determined using Lenz's Law, which states that the induced current will oppose the change in magnetic flux.

Step 2: Analyze the geometry of the L-shaped conductor. At t = 0 s, the enclosed area is zero, but as the moving conductor slides, the enclosed area increases. This change in area leads to a change in magnetic flux through the loop.

Step 3: Determine the direction of the magnetic field. The problem states that the magnetic field has a magnitude of 0.10 T. Assume the field is directed into the page (a common convention unless otherwise specified). This will help in applying Lenz's Law.

Step 4: Apply Lenz's Law to find the direction of the induced current. As the enclosed area increases, the magnetic flux through the loop increases. To oppose this increase, the induced current will create a magnetic field that opposes the external field. Using the right-hand rule, determine the direction of the induced current in the loop.

Step 5: Consider the resistance of the conductor. The resistance is given as 0.010 ohms per meter. This resistance will affect the magnitude of the induced current but not its direction. The direction of the current is determined solely by the change in magnetic flux and Lenz's Law.

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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 the circuit. The induced EMF is proportional to the rate of change of the magnetic flux. In this scenario, as the L-shaped conductor moves through the magnetic field, the area enclosed by the conductors changes, leading to a change in magnetic flux and thus inducing a 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 flux through the loop is increasing, the induced current will flow in a direction to create a magnetic field opposing that increase.

Right-Hand Rule

The Right-Hand Rule is a mnemonic used to determine the direction of the induced current and magnetic fields. For a current-carrying conductor in a magnetic field, if you point your thumb in the direction of the current and your fingers in the direction of the magnetic field, your palm will face the direction of the force experienced by the conductor. This rule helps visualize the relationship between current, magnetic field, and force.

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Textbook Question

CALC An electric generator has an 18-cm-diameter, 120-turn coil that rotates at 60 Hz in a uniform magnetic field that is perpendicular to the rotation axis. What magnetic field strength is needed to generate a peak voltage of 170 V?

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Textbook Question

INT A 20-cm-long, zero-resistance slide wire moves outward, on zero-resistance rails, at a steady speed of 10 m/s in a 0.10 T magnetic field. (See Figure 30.26.) On the opposite side, a 1.0 Ω carbon resistor completes the circuit by connecting the two rails. The mass of the resistor is 50 mg. If the wire is pulled for 10 s, what is the temperature increase of the carbon? The specific heat of carbon is 710 J/kg K.

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Textbook Question

A small, 2.0-mm-diameter circular loop with R = 0.020 Ω is at the center of a large 100-mm-diameter circular loop. Both loops lie in the same plane. The current in the outer loop changes from +1.0 A to −1.0 A in 0.10 s. What is the induced current in the inner loop?

Textbook Question

INT A 20-cm-long, zero-resistance slide wire moves outward, on zero-resistance rails, at a steady speed of 10 m/s in a 0.10 T magnetic field. (See Figure 30.26.) On the opposite side, a 1.0 Ω carbon resistor completes the circuit by connecting the two rails. The mass of the resistor is 50 mg. How much force is needed to pull the wire at this speed?

Textbook Question

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Textbook Question

A rectangular metal loop with 0.050 Ω resistance is placed next to one wire of the RC circuit shown in FIGURE P30.53. The capacitor is charged to 20 V with the polarity shown, then the switch is closed at t = 0 s. What is the current in the loop at t = 5.0 μs? Assume that only the circuit wire next to the loop is close enough to produce a significant magnetic field.

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