(a)
Find the expression for magnitudes of the magnetic field in each of the four layers.
(a)
Answer to Problem 27PQ
The expression for magnitudes of the magnetic field in each of the four layers are
Explanation of Solution
Write the expression for Ampere’s Law for the area bounded by the curve as.
Rearrange above equation for
Here,
Write the expression for current density as.
Here,
Write the expression for area of the circle as.
Substitute
Consider that the inner coaxial cable of radius
Write the expression for Amperian loop current as.
Substitute
Write the expression for Amperian loop is the circumferences of the circle as.
Substitute
Rearrange the above equation as.
Thus, the magnitude of the magnetic field in inner layer
Consider the inside insulator coaxial
The current in the loop is product of current density and area of loop is
The length of Ameprian loop is equal to the circumferences of the circle that is
Substitute
Thus, the magnitude of the magnetic field in inside insulator layer is
Consider the outer coaxial of radius
Write the current density of the layer
Substitute
Write the expression for Amperian loop current as.
Substitute
Substitute
Here,
Thus, the magnetic field on the third layer is
Write the expression for net magnetic field at the layer
Substitute
The net current enclosed inside the coaxial cable is zero.
Thus, the magnitude of the magnetic field outside the insulator layer is zero that is
Conclusion:
Thus, the expression for magnitudes of the magnetic field in each of the four layers are
(b)
Compare the part a results with the magnetic field produced by a long, straight wire and explain the advantage of using a coax.
(b)
Answer to Problem 27PQ
The expression for magnitude of the magnetic field for long straight current carrying wire is equal to the magnitude of the magnetic field in inside insulator layer.
Explanation of Solution
Write the expression for the magnetic field strength (magnitude) produced by a long straight current-carrying wire as.
The expression for long straight current carrying wire is equal to the magnitude of the magnetic field in inside insulator layer.
The advantage of using of coaxial cable as:
- 1. The inner conductor is in a Faraday shield, noise immunity is improved, and coax has lower error rates and therefore slightly better performance than twisted-pair.
- 2. Coax provides sufficient frequency range to support multiple channel, which allows for much greater throughput.
- 3. It also provides greater spacing between amplifiers coax's cable shielding reduces noise and crosstalk
Conclusion:
Thus, the expression for magnitude of the magnetic field for long straight current carrying wire is equal to the magnitude of the magnetic field in inside insulator layer.
Want to see more full solutions like this?
Chapter 31 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_forwardProblem 1: = 0.1 m. In the figure below four wires are on the corners of a square with a side of length L Each of the wires has a current I = 2 A. The wire on the bottom-left edge of the square has a current into the page. The remaining three wires on the square have a current out of the page. What is B at point P, the center of the square? Answer: B = Ho Ho¹ĵ = (8 × 10−6 T)î – (8 × 10− T)ĵ. πL πι I L √2 2 I L √2 L ·L/ 2 الله انکار L 12 I L 22 2 I Larrow_forwardQuestion #1. Consider a current-carrying circular wire with radius r. Find the angle between the infinitesimal length dl and some distance h? +z dl h dB +y y Current-carrying circular wire Note: radius r is perpendicular to the screen Select one: O 90° O 0° O 180° O 270°arrow_forward
- A coaxial cable consists of a solid center conducting wire and an outer coaxial cylindrical conductor. The space between the conductors and the outer insulation are made of a good insulating material e.g. neoprene. The figure below shows a cross section of such a cable. The current in the center wire is 2.47 A out of the page and the current in the outer conductor is 2.98 A into the page. If the distance a is 2.00 mm, determine the following. (a) the magnitude and direction of the magnetic field at the point P1. (b) the magnitude and direction of the magnetic field at the point P2arrow_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_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
- A (1.91x10^2)-mA current is used to charge up a parallel plate capacitor. A large square piece of paper is placed between the plates and parallel to them so it sticks out on all sides. What is the value of the integral P B. ds around the perimeter of the paper? Express your result in T.m with three significant figures.arrow_forwardChapter 32, Problem 006 A capacitor with square plates of edge length L is being discharged by a current of 0.59 A. The figure is a head-on view of one of the plates from inside the capacitor. A dashed rectangular path is shown. If L = 8.3 cm, W = 5.1 cm, and H = 2.4 cm, what is the value of ф8-ds around the dashed path?arrow_forwarda. b. For a current distribution in free space, Ã= (2x²y + y²)⸠+(xy² − xz³)â‚ − (6xyz – 2x²y²)⸠Wb/m . Show that A is a Maxwell's equation. Justify your answers. An x-y plane is an interface between two media. The interface carries current of 1/μ â, mA/m. The relative permeability for the regions are 6 and 4 respectively. The magnetic flux density of region with relative permeability of 4 is 5⸠+8â mWb/m². i. Sketch the interface between the two medium. ii. Analyse the media to determine the magnetic fields for both regions and magnetic flux density in the region with relative permeability of 6.arrow_forward
- The figure below is a cross-sectional view of a coaxial cable. The center conductor is surrounded by a rubber layer, an outer conductor, and another rubber layer. In a particular application, the current in the inner conductor is I1 = 1.12 A out of the page and the current in the outer conductor is I2 = 3.04 A into the page. Assuming the distance d = 1.00 mm, answer the following. PS:Please make sure your answer is in µTarrow_forwardA very long wire is bent in a circle as shown in the figure. The wire has current of 3 Amps flowing in the wire. What is the value of of the B field in unit of micro tesla due to the straight and wire at center point P? 1 = 200 Amps R= 4.14 cmarrow_forwardFigure 8 shows a coaxial cable (two nested cylinders) of length l, inner radius a and outer radius b. Note that l >> a and l >> b. The inner cylinder is charged to +Q and the outer cylinder is charged to −Q. The cable carries a current I, which flows clockwise. Use Ampere’s Law to calculate themagnetic field B⃗ at r<a, a<r<b, and r>b.arrow_forward
- Physics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage Learning