In earlier times when many households received nondigital television signals from an antenna, the lead-in wires from the antenna were often constructed in the form of two parallel wires (Fig. P31.50). The two wires carry currents of equal magnitude in opposite directions. The center-to-center separation of the wires is w, and a is their radius. Assume w is large enough compared with a that the wires carry the current uniformly distributed over their surfaces and negligible magnetic field exists inside the wires. (a) Why does this configuration of conductors have an inductance? (b) What constitutes the flux loop for this configuration? (c) Show that the inductance of a length x of this type of lead-in is
Figure P31.50
Want to see the full answer?
Check out a sample textbook solutionChapter 32 Solutions
EBK PHYSICS FOR SCIENTISTS AND ENGINEER
- Coaxial cables are used extensively for cable television and other electronic applications. A coaxial cable consists of two concentric cylindrical conductors. The region between the conductors is completely filled with polyethylene plastic as shown in 26.8a. Current leakage through the plastic, in the radial direction, is unwanted. (The cable is designed to conduct current along its length, but that is not the current being considered here.) The radius of the inner conductor is a = 0.500 cm, the radius of the outer conductor is b = 1.75 cm, and the length is L = 15.0 cm. The resistivity of the plastic is 1.0 x 1013 Ω ⋅ m. Calculate the radial resistance of the plastic between the two conductors.arrow_forwardIn earlier times when many households received nondigital television signals from an antenna, the lead-in wires from the antenna were often constructed in the form of two paral- lel wires (Fig. P31.50). The two wires carry currents of equal magnitude in opposite directions. The center-to-center separation of the wires is w, and a is their radius. Assume w is large enough compared with a that the wires carry the current uniformly distributed over their surfaces and negli- gible magnetic field exists inside the wires. (a) Why does this configuration of conductors have an inductance? (b) What TV antenna TV set Figure P31.50 constitutes the flux loop for this configuration? (c) Show that the inductance of a length x of this type of lead-in is w - a L In aarrow_forwardA portion of a long, cylindrical coaxial cable is shown in the figure below. An electrical current I = 3.0 amps flows down the center conductor, and this same current is returned in the outer conductor. Assume the current is distributed uniformly over the cross sections of the two parts of the cable. The values of the radii in the figure are r1 = 1.5 mm, r2 = 4.0 mm, and r3 = 7.0 mm. Using Ampere’s Law, find the magnitude of the magnetic field at the following distances from the center of the inner wire: a. 1.0 mm. b. 3.0 mm. c. 5.5 mm. d. 9.0 mm.arrow_forward
- Two very long coaxial cylindrical conductors are shown in cross-section below. The inner cylinder has radius a = 2 cm and caries a total current of I1 = 1.0 A in the positive z-direction (pointing out of the page). The outer cylinder has an inner radius b = 4 cm, outer radius c = 6 cm and carries a current of I2 = 2.0 A in the negative z-direction (pointing into the page). You may assume that the current is uniformly distributed over the cross-sectional area of the conductors. a) Calculate the magnitude and direction of the magnetic field at a radius of r=20 cm. b) Calculate the magnitude and direction of the magnetic field at a radius of r=3 cm.arrow_forwardProblem 7: A solenoid is created by wrapping a L = 35 m long wire around a hollow tube of diameter D = 4.5 cm. The wire diameter is d = 0.75 mm. The solenoid wire is then connected to a power supply so that a current of I = 4.5 A flows through the wire. Randomized Variables L= 35 m D= 4.5 cm d = 0.75 mm I= 4.5 A Part (a) Write an expression for the number of turns, N, in the solenoid. You do not need to take into account the diameter of the wire in this calculation. N = | 7 8 9. JT НOME d 1^ AL 4 5 6. a h 1 2 3 j k + END - m P VO BАСKSРАСE CLEAR DEL Submit Hint Feedback I give up! Part (b) Calculate the number of turns, N, in the solenoid. Part (c) Write an expression for the length of the solenoid (L2) in terms of the diameter of the hollow tube D, the length of the wire L and the diameter of the wire d. Assume it is constructed by using only 1 layer of loops (note that most solenoids are actually constructed with many layers, to maximize the magnetic field density). Part (d)…arrow_forwardA closed curve encircles several conductors. The line integral PB.dL around this curve is 3,83x104 T.m (a) What is the net current in the conductors? (b) If you were to integrate around the curve in the opposite direction, what would be the value of the line integral? Select one: lenci=D 305 A, 0.0 T.m lencl = 502 A, -3.83 x 10 4T.m lenci = 502 A, -7.66 x 104 T.m lencl = 600 A, -7.66 x 104T.m lencl = 305 A, -3.83 x 10 4 T.m lencl = 502 A, 0.0 T.m %3Darrow_forward
- Problem A wire of circular cross-section carries current density that is not uniform but varies with distance from the center asj(r)=j0(1-(r/R)2),for radius r in the range 0 < r < R. Here, j0 is a constant with units amperes per square meter, and the radius of the wire is R = 0.27 mm. Part (a) Find an expression for the current enclosed in a cylinder with a radius of r < R. Part (b) If the total current in the wire is I, find an expression for the constant j0, in terms of the other variables in the problem. Part (c) If the total current is 6.5 A, what is the constant j0, in amperes per square meter? Part (d) Find an expression for the magnetic field inside the wire, r < R, in terms of the current I. Part (e) For what r, in meters, is the magnetic field maximized? Part (f) What is the maximum value of the magnetic field, in tesla?arrow_forwardProblem 1: Two long thin parallel wires are 0.1 m apart and each wire carries a current of 12 A. The current for the wire on the left is into the page and the current for the wire on the right is out of the page. What is B at point P, 0.08 m from one wire and 0.06 m from the other wire? Hint: Point P is on the corner of the right triangle with the right angle. Answer: B = −(1.4 × 10−5 T)î − (4.8 × 10-5 T)ĵ. 0.08 m - X 0.1 m- I -0.06 marrow_forwardA long straight wire in the z-axis carries a current of 6.0 A in the positive z direction, and a circular loop of 10 cm radius in the xy-plane also carries 1.0-A current as shown in the figure. Point P in the center of the ring is 25 cm from the z-axis. An electron is ejected from P at a velocity of 1.0 × 106 m / s in the negative x direction. What is the y component of the force acting on the electron? (e = 1.60 × 10-19 C, μ0 = 4π × 10-7 T m / A)arrow_forward
- The xy-plane serves as the interface between two different media. Medium 1 (z 0) is filled with a material whose H, = 4. If the interface carries current (1/H) a, mA/m, and B, = 5a, + 8a, mWb/m², find H, and B,. a12 =a, K O H1 =6arrow_forward7. A sheet of copper foil 1 mm thick, 5 cm wide and 1.75 m long is connected to a voltage source as shown. There is a magnetic field B = 2.5 T into the page. Assume copper has conductivity σ = 5.96 x 107 mho/m and a charge carrier density n = 1028 electrons/m³. a) What is the current density J in the foil? b) What is the Hall voltage as measured by the voltmeter? c) Which point is at a higher potential, a or b? Voltmeter 20 Varrow_forward00:33 7.00 ,4GM KB/S 49% O wire -wire 2 de K.- l, - K.- l2- A current carrying wire(wire-1) with i1 = 10 Amperesis placed at the origin on the Y-Z plane. Another current carrying wire(wire-2) with i2 = 12 Amperesis placed l = 8 mdistance apart on the Y-axis. The point P2 is l1 = 6 mfrom the wire-1. P1 (0, 6, –6) P2 (0, 6,0) and the point P3 (0, 6, 7) are on the same line. The direction of the current is given in the figure. Step 1: Consider a wire-1 only. a) Calculate magnetic field at P x component Give your answer up to at least three significance digits. y component Give your answer up to at least three significance digits. z component Give your answer up to at least three significance digits. Calculate the magnetic field at P2 x component Give your answer up to at least three significance digits. y component Give your answer up to at least three significance digits. z component Give your answer up to at least three significance digits. Step 2:Consider both wires b)Now what is the…arrow_forward
- College PhysicsPhysicsISBN:9781305952300Author:Raymond A. Serway, Chris VuillePublisher:Cengage LearningUniversity Physics (14th Edition)PhysicsISBN:9780133969290Author:Hugh D. Young, Roger A. FreedmanPublisher:PEARSONIntroduction To Quantum MechanicsPhysicsISBN:9781107189638Author:Griffiths, David J., Schroeter, Darrell F.Publisher:Cambridge University Press
- Physics for Scientists and EngineersPhysicsISBN:9781337553278Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningLecture- Tutorials for Introductory AstronomyPhysicsISBN:9780321820464Author:Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina BrissendenPublisher:Addison-WesleyCollege Physics: A Strategic Approach (4th Editio...PhysicsISBN:9780134609034Author:Randall D. Knight (Professor Emeritus), Brian Jones, Stuart FieldPublisher:PEARSON