University:
Kentucky State University
Course:
PHY 212 | General Physics II
Academic year:

2019
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262

Pages:

17
Author:

Nossardisd7p

Chapter 29: Faraday’s Law Faraday’s Law of Induction Faraday’s Law of Induction Faraday’s Law of Induction dB  =− dt dB  = −N dt Faraday’s Law of Induction d  = − ( BA cos  ) dt Lenz’s Law dB  =− dt The induced current in a loop is in the direction that creates a magnetic field that opposes the change in magnetic flux through the area enclosed by the loop. Example 1: A coil consists of 200 turns of wire. Each turn is a square of side d = 18 cm, and a uniform magnetic field directed perpendicular to the plane of the coil is turned on. From t = 0 to t = 0.80 s, the field changes linearly from 0 to 0.50 T. (A) What is the magnitude of the induced emf in the coil between t = 0 and t = 0.80 s? For a constant rate of change (linear with time): 𝐵𝑓 − 𝐵𝑖 ΔΦ𝐵 Δ 𝐵𝐴 Δ𝐵 2 𝜀 =𝑁 =𝑁 = 𝑁𝐴 = 𝑁𝑑 Δ𝑡 Δ𝑡 Δ𝑡 Δ𝑡 0.50 T − 0 2 𝜀 = 200 0.18 m = 4.0 V 0.80 s (B) What is the magnitude of the induced current in the coil while the field is changing during the first 0.80 s? Assume the coil resistance is 2.0 . 𝜀 4.0 V 𝐼= = = 2.0 A 𝑅 2.0 Ω Example 2 A circular loop of wire of radius 12.0 cm is placed in a magnetic field directed perpendicular to the plane of the loop as shown in the Figure. If the field decreases at the rate of 0.050 T/s in some time interval, find the magnitude of the emf induced in the loop during this interval. For a constant rate of decrease: Example 3 The magnitude of the average emf is given by The average current induced in the coil is therefore Motional emf  F = 0  qE − qvB = 0  E = vB V = E = B v Motional emf B = B x dB d dx  =− = − ( B x) = −B   = −B v dt dt dt  B v I= = R R Motional emf: Energy Approach  =B v End-of-Chapter Problems 29.1 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. (a) What emf is induced in this loop? (b) If the loop has a resistance of 0.600  , find the current induced in the loop. 29.7 The current in the long, straight wire AB shown in Fig. E29.7 is upward and is increasing steadily at a rate di/dt. (a) At an instant when the current is i, what are the magnitude and direction of the field B at a distance r to the right of the wire? (b) What is the flux dB through the narrow, shaded strip? (c) What is the total flux through the loop? (d) What is the induced emf in the loop? (e) Evaluate the numerical value of the induced emf if a = 12.0 cm, b = 36.0 cm, L = 24.0 cm, and di/dt = 9.60 A/s. 29.27 Are Motional emfs a Practical Source of Electricity? How fast (in m/s and mph) would a 5.00-cm copper bar have to move at right angles to a 0.650-T magnetic field to generate 1.50 V (the same as a AA battery) across its ends? Does this seem like a practical way to generate electricity? 29.30 A 0.650-m-long metal bar is pulled to the right at a steady 5.0 m/s perpendicular to a uniform, 0.750-T magnetic field. The bar rides on parallel metal rails connected through a 25.0- resistor (Fig. E29.30), so the apparatus makes a complete circuit. Ignore the resistance of the bar and the rails. (a) Calculate the magnitude of the emf induced in the circuit. (b) Find the direction of the current induced in the circuit. (c) Calculate the current through the resistor. (b) Counterclockwise.

Chapter 29 Faraday’s Law

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