Ch 29: Electromagnetic Induction

Young & Freedman Calc - University Physics 14th Edition

Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610Not the one you use?Change textbook

Young & Freedman Calc 14th Edition

Ch 29: Electromagnetic Induction

Problem 19

Chapter 29, Problem 19

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.

Verified step by step guidance

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.

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.

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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Magnetic Flux

Related Practice

Textbook Question

A circular loop of wire with radius r = 0.0480 m and resistance R = 0.160 Ω is in a region of spatially uniform magnetic field, as shown in Fig. E29.22. The magnetic field is directed out of the plane of the figure. The magnetic field has an initial value of 8.00 T and is decreasing at a rate of dB/dt = -0.680 T/s. Is the induced current in the loop clockwise or counterclockwise?

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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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Textbook Question

A cardboard tube is wrapped with two windings of insulated wire wound in opposite directions, as shown in Fig. E29.20. Terminals a and b of winding A may be connected to a battery through a reversing switch. State whether the induced current in the resistor R is from left to right or from right to left in the following circumstances: (a) the current in winding Ais from a to b and is increasing; (b) the current in winding A is from b to a and is decreasing; (c) the current in winding A is from b to a and is increasing.

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Textbook Question

A circular loop of wire is in a region of spatially uniform magnetic field, as shown in Fig. E29.15. The magnetic field is directed into the plane of the figure. Determine the direction (clockwise or counterclockwise) of the induced current in the loop when (a) B is increasing; (b) B is decreasing; (c) B is constant with value B₀. Explain your reasoning.

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Textbook Question

The conducting rod ab shown in Fig. E29.29 makes contact with metal rails ca and db. The apparatus is in a uniform magnetic field of 0.800 T, perpendicular to the plane of the figure. In what direction does the current flow in the rod?

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Textbook Question

The current in Fig. $E 29.18$ obeys the equation $I (t) = I_{0} e^{- b t}$ , where $b is greater than 0$ . Find the direction (clockwise or counterclockwise) of the current induced in the round coil for $t is greater than 0$ .

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