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C31-33Worksheet2009

# C31-33Worksheet2009 - Worksheet 33 Three metal rods are...

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Unformatted text preview: Worksheet: Chapters 31, 32, 33 Three metal rods are placed on a horizontal table top, as shown at right. An upward magnetic field of strength B permeates the entire region. A metal crossbar of length l and mass m is placed on top of the parallel rods. The crossbar is pulled to the right at constant velocity v . The conducting path across the crossbar and through the three rods has resistance R . 1) At what rate is the magnetic flux through the circuit changing? d Blv dt Φ = 2) What is the magnitude and direction of the current moving through the crossbar? Blv i R = [toward you] 3) What force must be applied to the crossbar to maintain its motion? 2 2 B l v F R = [right] 4) At what rate is work being done by the applied force? 2 2 2 B l v P R = 5) At what rate is heat being produced in the circuit? 2 2 2 2 B l v P i R R = = Three metal rods are placed in a vertical plane, as shown at right. An inward magnetic field of strength B permeates the entire region. A metal crossbar of length l and mass m is placed in contact with the parallel rods. The crossbar is released from rest. The conducting path across the crossbar and through the three rods has resistance R . 6) If the speed of the crossbar at some instant is v , a) at what rate is the magnetic flux through the circuit changing? d Blv dt Φ = b) what is the magnitude and direction of the current moving through the crossbar? Blv i R = [right] c) what is the net force on the crossbar? 2 2 B l v F mg R =- [down] 7) What is the eventual final speed of the crossbar? 2 2 mgR v B l = [down] 8) What is the position of the crossbar as a function of its downward speed? Hint: ( 29 2 ln x dx B A Bx A A Bx A Bx- =--- - ∫ 2 ln g g v y g Av A A =- - where 2 2 B l A mR = x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x A long, straight wire carries a 5 A current to the right, as shown. A 50 cm by 50 cm square wire coil (mass m = 0.10 kg, resistance R = 1m Ω ) with N = 50 turns is moving away from the wire, downward in the diagram. At one instant in time, its top is 15 cm directly below the straight wire, moving at 2.5 m/s. 9) What is the magnetic flux through the square? 7.33 x 10-7 T·m 2 10) What is the voltage induced in a single wire at the top of the coil? 8.34 μ V 11) What is the voltage induced in a single wire at the bottom of the coil? 1.93 μ V 12) At what rate is the magnetic flux through the square changing? 6.41 μ V 13) What is the magnitude and direction of the current around the square?...
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C31-33Worksheet2009 - Worksheet 33 Three metal rods are...

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