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- Two 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_forwardThe homopolar generator, also called the Faraday disk, is a low-voltage, high-current electric generator. It consists of a rotating conducting disk with one stationary brush (a sliding electrical contact) at its axle and another at a point on its circumference as shown in Figure P23.21. A uniform magnetic field is applied perpendicular to the plane of the disk. Assume the field is 0.900 T, the angular speed is 3.20 103 rev/min, and the radius of the disk is 0.400 m. Find the emf generated between the brushes. When superconducting coils are used to produce a large magnetic field, a homopolar generator can have a power output of several megawatts. Such a generator is useful, for example, in purifying metals by electrolysis. If a voltage is applied to the output terminals of the generator, it runs in reverse as a homopolar motor capable of providing great torque, useful in ship propulsion.arrow_forwardAn election moves through a uniform electric field E = (2.50i + 5.00j) V/m and a uniform magnetic field B = 0.400k T. Determine the acceleration of the electron when it has a velocity v = 10.0i m/s.arrow_forward
- Why is the following situation impossible? A conducting rectangular loop of mass M = 0.100 kg, resistance R = 1.00 , and dimensions w = 50.0 cm by = 90.0 cm is held with its lower edge just above a region with a uniform magnetic field of magnitude B = 1.00 T as shown in Figure P30.34. The loop is released from rest. Just as the top edge of the loop reaches the region containing the field, the loop moves with a speed 4.00 m/s. Figure P30.34arrow_forwardA 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 conducting rod spans a gap of length L = 0.065 m and acts as the fourth side of a rectangular conducting loop, as shown in the figure. A constant magnetic field with magnitude B = 0.75 T pointing into the paper is in the region. The rod is pulled to the right by an external force, and moves with constant speed v = 0.015 m/s. The resistance in the wire is R = 180Ω. Part (a) Express the magnitude of the magnetic flux going through the loop, Φ, in terms of B, a and L. Part (b) Express the change in the magnetic flux, ΔΦ, in terms of B, L, v and Δt. Part (c) Express the magnitude of the average emf induced in the loop, ε, in terms of B, L, v. Part (d) Calculate the emf, in volts. Part (e) Express the current induced in the loop, I, in terms of ε and R.arrow_forward
- A nonconducting sphere has mass 80.0 g and radius 20.0 cm. A flat, compact coil ofwire with five turns is wrapped tightly around it, with each turn concentric with thesphere. The sphere is placed on an inclined plane that slopes downward to the left(Fig. P29.69), making an angle 0 with the horizontal so that the coil is parallel to theinclined plane. A uniform magnetic field of 0.350 T vertically upward exists in theregion of the sphere. (a) What current in the coil will enable the sphere to rest inequilibrium on the inclined plane? (b) Show that the result does not depend on thevalue of θ.arrow_forwardA straight, stiff wire of length 2.50 m and mass 56.0 g in the plane of the page is suspended in a magnetic field B = 0.710 T that points directly out of the page. The wire is connected to an emf. How much current must flow in the wire so that the wire is suspended and the tension in the supporting wires is zero?arrow_forwardThe current I through a long solenoid with n turns per meter and radius 0.30m is changing with time as given by I=sin(120t). The magnetic field inside a solenoid is given by B=nμ0I where μ0 is the free space permeability μ0=1.26·10−6 H/m. What is the magnetic flux through a single coil at a time of t= 1.1 s at distance r= 0.22 m from the center of the solenoid if there are, n=119 turns/m? a) Start by determining the flux through a gaussian loop of radius r=0.22 m centered in the middle of the solenoid. b) Next determine the rate of change of the magnetic flux with timearrow_forward
- A circular wire loop of radius rrr = 13 cmcm is immersed in a uniform magnetic field BBB = 0.555 TT with its plane normal to the direction of the field. If the field magnitude then decreases at a constant rate of −1.0×10−2 T/sT/s , at what rate should rr increase so that the induced emf within the loop is zero?arrow_forwardThe conducting rod shown in the figure 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 = 10cm, the speed of the is v = 6.2 m/s, and the magnitude of the magnetic field is B = 1.7 T. (a) What is the magnitude of emf induced in volts in the rod? (b) What is the current in amperes in the conducting loop? Assume that the resistance of the rod is 0.39 ohms and that the resistance of the rails and metal strip is negligibly small. (c) At what rate is the thermal energy being generated in the rod? (d) what force on the Rod is needed to maintain its velocity? (e) What is the work done by the force F?arrow_forwardA metal wire of mass m = 24.1 mg can slide with negligible friction on two horizontal parallel rails separated by distance d = 2.56 cm. The track lies in a vertical uniform magnetic field of magnitude 56.3 mT. At time t = 0, device G is connected to the rails, producing a constant current i = 9.13 mA in the wire and rails (even as the wire moves). At t = 61.1 ms, what are the wire’s (a) speed and (b) direction of motion (left or right)?arrow_forward
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