Physics for Scientists and Engineers: Foundations and Connections
1st Edition
ISBN: 9781133939146
Author: Katz, Debora M.
Publisher: Cengage Learning
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Chapter 32, Problem 23PQ
A square loop with side length L, mass M, and resistance R lies in the xy plane. A magnetic field
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In a certain region, the magnetic field is represented by the equation B = (a + bt)ĵ, where a = 3.50 mT and b = 4.00 mT/s. A
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A rod of length L = 10.0 cm that is forced to move at constant speed v = 5.00 m/s along horizontal rails. The rod, rails, and connecting strip at the right form a conducting loop. The rod has resistance 0.400 Ω; the rest of the loop has negligible resistance. A current i = 100 A through the long straight wire at distance a = 10.0 mm from the loop sets up a (nonuniform) magnetic field through the loop. Find the (a) emf and (b) current induced in the loop. (c) At what rate is thermal energy generated in the rod? (d) What is the magnitude of the force that must be applied to the rod to make it move at constant speed? (e) At what rate does this force do work on the rod?
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Express the magnitude of the magnetic flux going through the loop, Φ, in terms of A, t, a and θ.
a. Express the derivative of the flux with respect of time, dΦ/dt.
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Chapter 32 Solutions
Physics for Scientists and Engineers: Foundations and Connections
Ch. 32.1 - To calculate the magnetic flux through the...Ch. 32.2 - Prob. 32.2CECh. 32.3 - Prob. 32.3CECh. 32.3 - Prob. 32.4CECh. 32.4 - Prob. 32.5CECh. 32.5 - Prob. 32.6CECh. 32.6 - Prob. 32.7CECh. 32.8 - Prob. 32.8CECh. 32.8 - Prob. 32.9CECh. 32 - A constant magnetic field of 0.275 T points...
Ch. 32 - Prob. 2PQCh. 32 - Prob. 3PQCh. 32 - Prob. 4PQCh. 32 - Prob. 5PQCh. 32 - Figure P32.6 shows three situations involving a...Ch. 32 - A rectangular loop of length L and width W is...Ch. 32 - The magnetic field through a square loop of wire...Ch. 32 - Prob. 9PQCh. 32 - Prob. 10PQCh. 32 - Suppose a uniform magnetic field is perpendicular...Ch. 32 - Prob. 12PQCh. 32 - A square conducting loop with side length a = 1.25...Ch. 32 - A The magnetic field in a region of space is given...Ch. 32 - A The magnetic field in a region of space is given...Ch. 32 - Prob. 16PQCh. 32 - Prob. 17PQCh. 32 - Prob. 18PQCh. 32 - A square loop with side length 5.00 cm is on a...Ch. 32 - A thin copper rod of length L rotates with...Ch. 32 - Figure P32.21 shows a circular conducting loop...Ch. 32 - Prob. 22PQCh. 32 - A square loop with side length L, mass M, and...Ch. 32 - Prob. 24PQCh. 32 - Prob. 25PQCh. 32 - Prob. 26PQCh. 32 - Prob. 27PQCh. 32 - A solenoid of area Asol produces a uniform...Ch. 32 - Two circular conductors are perpendicular to each...Ch. 32 - Two circular conducting loops labeled A and B are...Ch. 32 - Prob. 31PQCh. 32 - Prob. 32PQCh. 32 - Prob. 33PQCh. 32 - Prob. 34PQCh. 32 - Prob. 35PQCh. 32 - Find an expression for the current in the slide...Ch. 32 - The slide generator in Figure 32.14 (page 1020) is...Ch. 32 - Prob. 38PQCh. 32 - A thin conducting bar (60.0 cm long) aligned in...Ch. 32 - A stiff spring with a spring constant of 1200.0...Ch. 32 - A generator spinning at a rate of 1.20 103...Ch. 32 - Suppose you have a simple homemade AC generator...Ch. 32 - Prob. 43PQCh. 32 - Prob. 44PQCh. 32 - Prob. 45PQCh. 32 - Prob. 46PQCh. 32 - A square coil with a side length of 12.0 cm and 34...Ch. 32 - Prob. 48PQCh. 32 - Prob. 49PQCh. 32 - Prob. 50PQCh. 32 - Prob. 51PQCh. 32 - Prob. 52PQCh. 32 - Prob. 53PQCh. 32 - Prob. 54PQCh. 32 - Prob. 55PQCh. 32 - Prob. 56PQCh. 32 - Prob. 57PQCh. 32 - A step-down transformer has 65 turns in its...Ch. 32 - Prob. 59PQCh. 32 - Prob. 60PQCh. 32 - Prob. 61PQCh. 32 - Prob. 62PQCh. 32 - Prob. 63PQCh. 32 - A bar magnet is dropped through a loop of wire as...Ch. 32 - Prob. 65PQCh. 32 - Prob. 66PQCh. 32 - A circular coil with 75 turns and radius 12.0 cm...Ch. 32 - Each of the three situations in Figure P32.68...Ch. 32 - A square loop with sides 1.0 m in length is placed...Ch. 32 - Prob. 70PQCh. 32 - Two frictionless conducting rails separated by l =...Ch. 32 - Imagine a glorious day after youve finished...Ch. 32 - Prob. 73PQCh. 32 - A Figure P32.74 shows an N-turn rectangular coil...Ch. 32 - A rectangular conducting loop with dimensions w =...Ch. 32 - Prob. 76PQCh. 32 - A conducting rod is pulled with constant speed v...Ch. 32 - Prob. 78PQCh. 32 - A conducting single-turn circular loop with a...Ch. 32 - A metal rod of mass M and length L is pivoted...
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- A conducting single-turn circular loop with a total resistance of 5.00 is placed in a time-varying magnetic field that produces a magnetic flux through the loop given by B = a + bt2 ct3, where a = 4.00 Wb, b = 11.0 Wb/s2, and c = 6.00 Wb/s3. B is in webers, and t is in seconds. What is the maximum current induced in the loop during the time interval t = 0 to t = 3.50 s?arrow_forwardA circular loop of wire with a radius of 4.0 cm is in a uniform magnetic field of magnitude 0.060 T. The plane of the loop is perpendicular to the direction of the magnetic field. In a time interval of 0.50 s, the magnetic field changes to the opposite direction with a magnitude of 0.040 T. What is the magnitude of the average emf induced in the loop? (a) 0.20 V (b) 0.025 V (c) 5.0 mV (d) 1.0 mV (e) 0.20 mVarrow_forwardA flat loop of wire consisting of a single turn of cross-sectional area 8.00 cm2 is perpendicular to a magnetic field that increases uniformly in magnitude from 0.500 T to 2.50 T in 1.00 s. What is the resulting induced current if the loop has a resistance of 2.00 ?arrow_forward
- A rectangular conducting loop with dimensions w = 32.0 cm and h = 78.0 cm is placed a distance a = 5.00 cm from a long, straight wire carrying current I = 7.00 A in the downward direction (Fig. P32.75). a. What is the magnitude of the magnetic flux through the loop? b. If the current in the wire is increased linearly from 7.00 A to 15.0 A in 0.230 s, what is the magnitude of the induced emf in the loop? c. What is the direction of the current that is induced in the loop during this time interval?arrow_forwardThe square armature coil of an alternating current generator has 200 turns and is 20.0 cm on side. When it rotates at 3600 rpm, its peak output voltage is 120 V. (a) Wliat is the frequency' of the output voltage? (b) What is the strength of the magnetic field in which the coil is turning?arrow_forwardTwo frictionless conducting rails separated by l = 55.0 cm are connected through a 2.00- resistor, and the circuit is completed by a bar that is free to slide on the rails (Fig. P32.71). A uniform magnetic field of 5.00 T directed out of the page permeates the region, a. What is the magnitude of the force Fp that must be applied so that the bar moves with a constant speed of 1.25 m/s to the right? b. What is the rate at which energy is dissipated through the 2.00- resistor in the circuit?arrow_forward
- You wish to move a rectangular loop of wire into a region of uniform magnetic field at a given speed so as to induce an emf in the loop. The plane of the loop must remain perpendicular to the magnetic field lines. In which orientation should you hold the loop while you move it into the region of magnetic field so as to generate the largest emf? (a) with the long dimension of the loop parallel to the velocity vector (b) with the short dimension of the loop parallel to the velocity vector (c) either way because the emf is the same regardless of orientationarrow_forwardA 500-turn coil with a 0.250m2 area is spun in Earth’s 5.00105T magnetic field, producing a 12.0-kV maximum emf. (a) As what angular velocity must the coil be spun? (b) What is unreasonable about this result? (c) Which assumption or premise is responsible?arrow_forwardA wire is bent in the form of a square loop with sides of length L (Fig. P30.24). If a steady current I flows in the loop, determine the magnitude of the magnetic field at point P in the center of the square. FIGURE P30.24arrow_forward
- A rectangular toroid with inner radius R1= 7.0cm, outer radius R2= 9.0cm, height h = 3.0, and N=3.0, and N = 3000 turns is filled with an iron core a magnetic susceptibility 5.2 × 103. (a) What is the self-inductance of the toroid? (b) If the current through the toroid is 2.0 A, what is the magnetic field at the center of the core? (c) For this same 2.0-A current, what is the effective surface current formed by the aligned atomic current loops in the iron core?arrow_forwardA toroid has a major radius R and a minor radius r and is tightly wound with N turns of wire on a hollow cardboard torus. Figure P31.6 shows half of this toroid, allowing us to see its cross section. If R r, the magnetic field in the region enclosed by the wire is essentially the same as the magnetic field of a solenoid that has been bent into a large circle of radius R. Modeling the field as the uniform field of a long solenoid, show that the inductance of such a toroid is approximately L=120N2r2R Figure P31.6arrow_forwardIn Figure P30.38, the rolling axle, 1.50 m long, is pushed along horizontal rails at a constant speed v = 3.00 m/s. A resistor R = 0.400 is connected to the rails at points a and b, directly opposite each other. The wheels make good electrical contact with the rails, so the axle, rails, and R form a closed-loop circuit. The only significant resistance in the circuit is R. A uniform magnetic field B = 0.080 0 T is vertically downward. (a) Find the induced current I in the resistor. (b) What horizontal force F is required to keep the axle rolling at constant speed? (c) Which end of the resistor, a or b, is at the higher electric potential? (d) What If? After the axle rolls past the resistor, does the current in R reverse direction? Explain your answer. Figure P30.38arrow_forward
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What is Electromagnetic Induction? | Faraday's Laws and Lenz Law | iKen | iKen Edu | iKen App; Author: Iken Edu;https://www.youtube.com/watch?v=3HyORmBip-w;License: Standard YouTube License, CC-BY