ASSIGNMENT #13

DUE ON DECEMBER 8, 2005

HAND-IN

CHAPTER #29:

QUESTIONS:

PROBLEMS:

86 Figure 29-84 is an idealized schematic drawing of a rail gun. Projectile P sits between two wide rails of circular cross section; a source of current sends current through the rails and through the (conducting) projectile (a fuse is not used). (a) Let w be the distance between the rails, R the radius of each rail, and i the current. Show that the force on the projectile is directed to the right along the rails and is given approximately by

(b) If the projectile starts from the left end of the rails at rest, find the speed v at which it is expelled at the right. Assume that i = 450 kA, w = 12 mm, R = 6.7 cm, L = 4.0 m, and the projectile mass is 10 g.

CHAPTER #30:

QUESTIONS:

3 Figure 30-27 shows two circuits in which a conducting bar is slid at the same speed v through the same uniform magnetic field and along a -shaped wire. The parallel lengths of the wire are separated by 2L in circuit 1 and by L in circuit 2. The current induced in circuit 1 is counterclockwise. (a) Is the magnetic field into or out of the page? (b) Is the current induced in circuit 2 clockwise or counterclockwise? (c) Is the emf induced in circuit 1 larger than, smaller than, or the same as that in circuit 2?

PROBLEMS:

••15   In Figure 30-44, a stiff wire bent into a semicircle of radius a = 2.0 cm is rotated at constant angular speed 40 rev/s in a uniform 20 mT magnetic field. What are the (a) frequency and (b) amplitude of the emf induced in the loop?

•••22   For the wire arrangement in Figure 30-48, a = 12.0 cm and b = 16.0 cm. The current in the long straight wire is given by i = 4.50t² – 10.0t, where i is in amperes and t is in seconds. (a) Find the emf in the square loop at t = 3.00 s. (b) What is the direction of the induced current in the loop?

••32 In Figure 30-54, two straight conducting rails form a right angle. A conducting bar in contact with the rails starts at the vertex at time t = 0 and moves with a constant velocity of 5.20 m/s along them. A magnetic field with B = 0.350 T is directed out of the page. Calculate (a) the flux through the triangle formed by the rails and bar at t = 3.00 s and (b) the emf around the triangle at that time. (c) If the emf is = atⁿ, where a and n are constants, what is the value of n?

ONLINE

CHAPTER #30:

QUESTIONS:

PROBLEMS:

••11 A rectangular coil of N turns and of length a and width b is rotated at frequency f in a uniform magnetic field , as indicated in Figure 30-42. The coil is connected to co-rotating cylinders, against which metal brushes slide to make contact. (a) Show that the emf induced in the coil is given (as a function of time t) by

This is the principle of the commercial alternating-current generator. (b) What value of Nab gives an emf with ₀ = 150 V when the loop is rotated at 60.0 rev/s in a uniform magnetic field of 0.500 T?

••31 The conducting rod shown in Figure 30-52 has length L and is being pulled along horizontal, frictionless conducting rails at a constant velocity . The rails are connected at one end with a metal strip. A uniform magnetic field , directed out of the page, fills the region in which the rod moves. Assume that L = 10 cm, v = 5.0 m/s, and B = 1.2 T. What are the (a) magnitude and (b) direction (up or down the page) of the emf induced in the rod? What are the (c) size and (d) direction of the current in the conducting loop? Assume that the resistance of the rod is 0.40 W and that the resistance of the rails and metal strip is negligibly small. (e) At what rate is thermal energy being generated in the rod? (f) What external force on the rod is needed to maintain ? (g) At what rate does this force do work on the rod

CHAPTER #32:

QUESTIONS:

PROBLEMS:

••16   The magnitude of the electric field between the two circular parallel plates in Figure 32-30 is E = (4.0 × 10⁵) – (6.0 × 10⁴t), with E in volts per meter and t in seconds. At t = 0, is upward. The plate area is 4.0 × 10^–2 m². For t ≥ 0, what are the (a) magnitude and (b) direction (up or down) of the displacement current between the plates and (c) is the direction of the induced magnetic field clockwise or counterclockwise in the figure?

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