We have seen that a long solenoid produces a uniform magnetic field directed along the axis of a cylindrical region. To produce a uniform magnetic field directed parallel to a diameter of a cylindrical region, however, one can use the saddle coils illustrated in Figure P29.46. The loops are wrapped over a long, somewhat flattened tube. Figure P29.46a shows one wrapping of wire around the tube. This wrapping is continued in this manner until the visible side has many long sections of wire carrying current to the left in Figure P29.46a and the back side has many lengths carrying current to the right. The end view of the tube in Figure P29.46b shows these wires and the currents they carry. By wrapping the wires carefully, the distribution of wires can take the shape suggested in the end view such that the overall current distribution is approximately the superposition of two overlapping, circular cylinders of radius R (shown by the dashed lines) with uniformly distributed current, one toward you and one away from you. The current density J is the same for each cylinder. The center of one cylinder is described by a position vector
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Chapter 29 Solutions
Physics for Scientists and Engineers
- For both sketches in Figure P30.56, there is a 3.54-A current, a magnetic field strength B 0.650 T. and the angle is 32.0. Find the magnetic force per unit length (magnitude and direction) exerted on the current-carrying conductor in both cases.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_forwardA wire carrying a current I is bent into the shape of an exponential spiral, r = e, from = 0 to = 2 as suggested in Figure P29.47. To complete a loop, the ends of the spiral are connected by a straight wire along the x axis. (a) The angle between a radial line and its tangent line at any point on a curve r = f() is related to the function by tan=rdr/d Use this fact to show that = /4. (b) Find the magnetic field at the origin. Figure P29.47arrow_forward
- Two infinitely long current-carrying wires run parallel in the xy plane and are each a distance d = 11.0 cm from the y axis (Fig. P30.83). The current in both wires is I = 5.00 A in the negative y direction. a. Draw a sketch of the magnetic field pattern in the xz plane due to the two wires. What is the magnitude of the magnetic field due to the two wires b. at the origin and c. as a function of z along the z axis, at x = y = 0? FIGURE P30.83arrow_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_forwardFigure P23.15 shows a top view of a bar that can slide on two frictionless rails. The resistor is R = 6.00 , and a 2.50-T magnetic field is directed perpendicularly downward, into the paper. Let = 1.20 m. (a) Calculate the applied force required to move the bar to the right at a constant speed of 2.00 m/s. (b) At what rate is energy delivered to the resistor? Figure P23.15 Problems 15 through 18.arrow_forward
- 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 P30.38arrow_forwardThe triangular loop of wire shown in Figure P30.62 carries a current of 0.125 A, and a uniform magnetic field of 0.250 T points toward the right. Determine the force on each segment of the wire (indicate magnitude and direction) and the net force on the triangular loop.arrow_forwardA constant magnetic field of 0.275 T points through a circular loop of wire with radius 3.50 cm as shown in Figure P32.1. a. What is the magnetic flux through the loop? b. Is a current induced in the loop? Explain. FIGURE P32.1arrow_forward
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