29.7 CALC The current in the Figure E29.7 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 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 В -dr L a the induced emf if a = 12.0 cm, 24.0 cm, and di/dt = 9.60 A/s. b 36.0 cm, L Figure P29.51
29.51 In Fig. P29.51 the loop is being pulled to the right at constant speed v. A constant current I flows in the long wire, in the direction shown.
(a) Calculate the magnitude of the net emf induced in the loop. Do this two ways:
(i) by using Faraday’s law of induction (Hint: See Exercise 29.7) and
(ii) by looking at the emf induced in each segment of the loop due to its motion.
(b) Find the direction (clockwise or counterclockwise) of the current induced in the loop. Do this two ways:
(i) using Lenz’s law and
(ii) using the magnetic force on charges in the loop.
(c) Check your answer for the emf in part (a) in the following special cases to see whether it is physically reasonable:
(i) The loop is stationary:
(ii) the loop is very thin, so a reaches 0;
(iii) the loop gets very far from the wire.
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