The figure shows a rod of length L - 12.8 cm that is forced to move at constant speed v= 5.80 m/s along horizontal rails. The rod, rails, and connecting strip at the right form a conducting loop. The rod has resistance 0.581 02; the rest of the loop has negligible resistance. A current i = 140 A through the long straight wire at distance a 13.8 mm from the loop sets up a (nonuniform) magnetic field throughout loop. Find the (a) magnitude of the 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? wwwg a + X X X . X X X X • .. . . • e . . < . X ● . . • ● X ● . . . . · . ● · B ● . ● · ·

The figure shows a rod of length L - 12.8 cm that is forced to move at constant speed v= 5.80 m/s along horizontal rails. The rod, rails, and connecting strip at the right form a conducting loop. The rod has resistance 0.581 02; the rest of the loop has negligible resistance. A current i = 140 A through the long straight wire at distance a 13.8 mm from the loop sets up a (nonuniform) magnetic field throughout loop. Find the (a) magnitude of the 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? wwwg a + X X X . X X X X • .. . . • e . . < . X ● . . • ● X ● . . . . · . ● · B ● . ● · ·

Physics for Scientists and Engineers with Modern Physics

10th Edition

ISBN:9781337553292

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter30: Faraday's Law

Section: Chapter Questions

Problem 38AP: In Figure P30.38, the rolling axle, 1.50 m long, is pushed along horizontal rails at a constant...

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Consider the apparatus shown in Figure P30.32: a conducting bar is moved along two rails connected to an incandescent lightbulb. The whole system is immersed in a magnetic field of magnitude B = 0.400 T perpendicular and into the page. The distance between the horizontal rails is = 0.800 m. The resistance of the lightbulb is R = 48.0 , assumed to be constant. The bar and rails have negligible resistance. The bar is moved toward the right by a constant force of magnitude F = 0.600 N. We wish to find the maximum power delivered to the lightbulb. (a) Find an expression for the current in the lightbulb as a function of B, , R, and v, the speed of the bar. (b) When the maximum power is delivered to the lightbulb, what analysis model properly describes the moving bar? (c) Use the analysis model in part (b) to find a numerical value for the speed v of the bar when the maximum power is being delivered to the lightbulb. (d) Find the current in the lightbulb when maximum power is being delivered to it. (e) Using P = I2R, what is the maximum power delivered to the lightbulb? (f) What is the maximum mechanical input power delivered to the bar by the force F? (g) We have assumed the resistance of the lightbulb is constant. In reality, as the power delivered to the lightbulb increases, the filament temperature increases and the resistance increases. Does the speed found in part (c) change if the resistance increases and all other quantities are held constant? (h) If so, does the speed found in part (c) increase or decrease? If not, explain. (i) With the assumption that the resistance of the lightbulb increases as the current increases, does the power found in part (f) change? (j) If so, is the power found in part (f) larger or smaller? If not, explain. Figure P30.32
In 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 P30.38
The figure shows a rod of length L = 8.77 cm that is forced to move at constant speed v = 5.17 m/s along horizontal rails. The rod, rails, and connecting strip at the right form a conducting loop. The rod has resistance 0.498 2; the rest of the loop has negligible resistance. A current i = 117 A through the long straight wire at distance a = 9.27 mm from the loop sets up a (nonuniform) magnetic field throughout loop. Find the (a) magnitude of the 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? X X X X X X X ● X X X ● ● · X XX X X ● ● • ● ● B • X
The figure shows a rod of length L = 12.6 cm that is forced to move at constant speed v = 5.39 m/s along horizontal rails. The rod, rails, and connecting strip at the right form a conducting loop. The rod has resistance 0.488 0; the rest of the loop has negligible resistance. A current i = 120 A through the long straight wire at distance a = 8.65 mm from the loop sets up a (nonuniform) magnetic field throughout loop. Find the (a) magnitude of the 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? x x (a) Number i (b) Number i (c) Number i (d) Number i (e) Number Units Units Units Units Units @ .. Ⓡ • • " XX .. .. . • • . > > <
The long straight wire in the figure has current I = 1 A flowing in it. A square loop which has 10-cm sides is positioned 10 cm away from the wire as shown. The loop is then moved in the positive x-direction with a speed v = 10 cm/s. If the loop has a resistance of 0.02 ohms, calculate the direction and the magnitude of the net force acting on the loop the instant the loop is made to move.
The figure shows a rod of length L = 12.6 cm that is forced to move at constant speed v = 5.39 m/s along horizontal rails. The rod, rails, and connecting strip at the right form a conducting loop. The rod has resistance 0.488 0; the rest of the loop has negligible resistance. A current i = 120 A through the long straight wire at distance a = 8.65 mm from the loop sets up a (nonuniform) magnetic field throughout loop. (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? (d) Number (e) Number i Units Units xx @ xx .. Ⓡ x • • " XX .. .. . • • <
A conducting bar of length moves to the right on two frictionless rails as shown in the figure below. A uniform magnetic field directed into the page has a magnitude of 0.310 T. Assume R = 8.70 and l = 0.340 m. l R * xxxxxx x x X x counterclockwise into the page out of the page x x x Bin (a) At what constant speed should the bar move to produce an 8.20-mA current in the resistor? m/s (b) What is the direction of the induced current? clockwise (c) At what rate is energy delivered to the resistor? mW
A conducting rod of length = 65.0 cm is free to slide on two parallel conducting bars as shown in the figure below. Two resistors R1 = 6.00 Q and R2 = 9.00 Q are connected across the ends of the bars to form a loop. A constant magnetic field B = 10.0 T is directed perpendicularly into the page. An external agent pulls the rod to the left with a constant speed of v = 4.00 m/s. * x x × in R R2 х х х х a) What is the magnitude and direction (positive terminal upward or positive terminal downward) of the emf induced in the moving rod? Think about which direction current will flow on the rod and remember current flows out of the positive end of a battery. b) Calculate the magnitude and direction (upward or downward) of the induced currents through each of two the resistors. c) Calculate the total power delivered to the resistors in the circuit. d) What is the magnitude of the external force required to keep the bar moving to the left at the constant speed of 4.00 m/s?
A conducting rod of length ℓ = 35.0 cm is free to slide on two parallel conducting bars as shown in the figure below. Two resistors R1 = 2.00 Ω and R2 = 5.00 Ω are connected across the ends of the bars to form a loop. A constant magnetic field B = 2.90 T is directed perpendicularly into the page. An external agent pulls the rod to the left with a constant speed of v = 7.80 m/s. Find the following. a) the currents in both resistors b) the total power delivered to the resistance of the circuit c) the magnitude of the applied force that is needed to move the rod with this constant velocity
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?
A conducting rod of length = 65.0 cm is free to slide on two parallel conducting bars as shown in the figure below. Two resistors R₁ = 6.00 2 and R₂ = 9.00 2 are connected across the ends of the bars to form a loop. A constant magnetic field B = 10.0 T is directed perpendicularly into the An external agent pulls the rod to the left with a constant speed of v = 4.00 m/s. page. R₁ xxx x xx xx x xxx X X S x x X x x x x x X
A circular coil of 20 turns and radius 5.0 cm is placed with its plane oriented at 90° to a uniform magnetic field of 0.10 T. The field is now increased at a steady rate, reaching a value of 0.50 T after 4.0 seconds. What emf is induced in the coil? O 0.031 V O 0.021 V O 0.026 V O 0.016 V O 0.036 V