(a) Explanation Given Info : The number of turns N of the coil is 4 . The radius r of the coil is 0.800 cm . The resistance R of the coil is 0.250 Ω . Formula to calculate the magnitude of induced emf by Faraday’s law is, ε ind = | N d Φ B d t | d Φ B d t is the rate of change of magnetic flux. Formula to calculate the magnetic flux is, Φ B = B A B is the uniform magnetic field, A is the area of the coil. Substitute B A for Φ B to find ε ind . ε ind = | N d ( B A ) d t | = A N | d B d t | (I) Formula to calculate the induced emf by ohm’s law is, V = I R I is the current through the coil, R is the resistance of the coil. Substitute ε ind for V , since it is caused by the change in flux. ε ind = I R Substitute I R for ε ind in equation (I). I R = A N | d B d t | I R = ( A N ) ( d B d t ) Rearrange the above equation as follows, d B d t = R I A N Using the method of separation of variables for the above equation, d B = I R A N d t Let us consider the change in magnetic field d B is represented by Δ B for the above equation as follows, Δ B = I R A N d t Take integration for the above equation with time limits varies from 0 to t as follows, Δ B = ∫ 0 t I R A N d t = R A N ∫ 0 t I d t (II) Refer figure.2. Take a time t limit varies from 0 to 2.00 s for the equation (II) is, Δ B 0 → 2 = R A N ∫ 0 2.00 s I d t Formula to calculate the integral area of current under the curve for the time t varies from 0 to 2.00 s in the i versus t graph is, ∫ 0 2.00 s I d t = ( 1 2 ) b h (III) b is the breadth of the area along t axis, h is the height of the area along i axis. Substitute ( 2.00 s − 0.0 s ) for b and 3.00 mA for h in equation (III). ∫ 0 2.00 s I d t = ( 1 2 ) ( 2 (b) To determine The magnetic field at the location of the coil for the time t is 5.00 s . (c) To determine The magnetic field at the location of the coil for the time t is 6.00 s .

University Physics with Modern Physics (14th Edition)

14th Edition

ISBN: 9780321973610

Author: Hugh D. Young, Roger A. Freedman

Publisher: PEARSON

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Question

Chapter 29, Problem 29.66P

(a)

To determine

The magnetic field at the location of the coil for the time t is 2.00 s .

(b)

To determine

The magnetic field at the location of the coil for the time t is 5.00 s .

(c)

To determine

The magnetic field at the location of the coil for the time t is 6.00 s .

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Chapter 29, Problem 29.65P

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Chapter 29 Solutions

University Physics with Modern Physics (14th Edition)

Ch. 29.2 - The accompanying figure shows a wire coil being...Ch. 29.3 - (a) Suppose the magnet in Fig. 29.14a were...Ch. 29.4 - The earths magnetic field points toward (magnetic)...Ch. 29.5 - If you wiggle a magnet back and forth in your...Ch. 29.6 - Prob. 29.6TYU Ch. 29.7 - Prob. 29.7TYU Ch. 29 - A sheet of copper is placed between the poles of...Ch. 29 - Prob. 29.2DQ Ch. 29 - Prob. 29.3DQ Ch. 29 - Prob. 29.4DQ

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