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
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- 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_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_forwardTwo 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_forward
- Problem 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_forwardHELPPParrow_forwardThe 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_forward
- A 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_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_forwardA hollow copper tube carries a current along its length. Why is B = 0 inside the tube? Is B nonzero outside the tube?arrow_forward
- A silver wire has resistivity p = 1.60 × 108 Q-m and a cross-sectional area of 2.20 mm2. The current in the wire is uniform and changing at the rate of 2850 A/s when the current is 180 A. (a) What is the magnitude of the (uniform) electric field in the wire when the current in the wire is 180 A? (b) What is the displacement current in the wire at that time? (c) What is the ratio of the magnitude of the magnetic field due to the displacement current to that due to the current at a distance r from the wire? (a) Number i Units (b) Number i Units (c) Number i Unitsarrow_forwardA (8.42x10^-1)-m radius cylindrical region contains a uniform electric field along the cylinder axis. It is increasing uniformly with time. What is the rate of change (magnitude) of the electric field required to obtain a total displacement current of (2.047x10^0) nA through a cross section of the region? Provide your answer in V/(m.s) with three significant figures.arrow_forwardA (7.4020x10^-1)-m radius cylindrical region contains a uniform electric field that is parallel to the axis and is increasing at the rate (3.24x10^12) V/mxs. What is the magnitude of the magnetic field at a point (2.0320x10^-1) m from the axis? Express your result with three significant figures.arrow_forward
- Physics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage LearningPrinciples of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning