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6. (20 points) A coaxial cable consists of an infinitely long thin wire carrying a charge...
A coaxial cable is formed by a long, straight wire and a hollow conducting cylinder with...
A coaxial cable is formed by a long, straight wire and a hollow conducting cylinder with axes that coincide. The wire has charge per unit length λ = 7λ0, and the hollow cylinder has net charge per unit length λ = 6λ0. Use Gauss's law to answer these questions: What are the charges per unit length on the following surfaces of the hollow cylinder? (a) the inner surface (Use the following as necessary: λ0.) λinner = (b) the outer...
An infinitely long straight wire is uniformly charged with a positive linear charge density +?. It...
An infinitely long straight wire is uniformly charged with a
positive linear charge density +?. It is surrounded by an
insulating hollow cylinder (also infinitely long) of inner radius R
and outer radius 2R. The hollow cylinder has a uniform charge
density ?.
(a) Determine the value of ? if the electric field vanishes at
every point outside the cylinder (r > 2R).
(b) Determine the electric field in the region 0 < r <
R.
(c) Determine the electric...
18. A infinitely long cable consists of a solid cylindrical inner conductor of radius a, surrounded...
18. A infinitely long cable consists of a solid cylindrical inner conductor of radius a, surrounded by a concentric cylindrical conducting shell of inner radius b and outer radius c. The inner conductor has a non-uniform current density (r) = ar in the z direction shown. a is a positive constant with units A-m'. The outer conductor has a uniform current density: Jr) = -B (in negative z). B has the same unit as a. The conductors carry equal and...
An infinitely long, thin wire has a known current of 2i, which flows in the negative...
An infinitely long, thin wire has a known current of 2i, which flows in the negative x-direction. It is surrounded by an infinitely long, hollow cylindrical wire so the wires have a common axis. The hollow wire has inner radius A and outer radius B. A known current i, which is uniformly spread over the hollow wire, flows in the positive x-direction in the hollow cylindrical wire. Cross-Section View A 2i i 0 +x 2 Z B +x What is...
An infinitely long straight wire has a uniform linear charge density of λ. Derive the equation...
An infinitely long straight wire has a uniform linear charge density of λ. Derive the equation for the electric field a distance R away from the wire using Gauss's Law for Electrostatics.
An infinitely long, thin wire has a known current of 2i, which flows in the negative...
An infinitely long, thin wire has a known current of 2i, which flows in the negative x-direction. It is surrounded by an infinitely long, hollow cylindrical wire so the wires have a common axis. The hollow wire has inner radius A and outer radius B. A known current i, which is uniformly spread over the hollow wire, flows in the positive x-direction in the hollow cylindrical wire. Cross-Section View A 21 0 +x 2 Z B 210. +x ♡ What...
4. Consider an infinitely long, thin, uniformly charged wire length. Symmetry dictates that the e...
4. Consider an infinitely long, thin, uniformly charged wire length. Symmetry dictates that the electric field in cylindrical coordinates will have only an r component (i.e. no θ or k components). Use the superposition principle to show that the electric field in cylindrical coordinates is with charge density λ per unit (4.63) 2 Hint: You will find the integral useful 2 )3/2 5. Find an expression for the voltage field around the wire in question 4.
4. Consider an infinitely...
6. (3 points) A coaxial cable consists of a solid inner conductor of radius Ri, surrounded...
6. (3 points) A coaxial cable consists of a solid inner conductor of radius Ri, surrounded by a concentric cylindrical tube of inner radius R2 and outer radius Rs (called the shield) as shown in Figure 8. The conductors carry equal and opposite currents, I, distributed uniformly across their cross sections. Determine the magnetic field at a distance r from the axis for: (a) r< Ri (b) Ri < R2 Page 2 (c) R2<r<Rs (d) R3 (e) Plot the magnitude...
This coaxial cable consists of a solid inner conductor of radius ?1 and a very thin...
This coaxial cable consists of a solid inner conductor of radius ?1 and a very thin outer conductor of radius ?2. The two cables carry equal currents ?, but in the opposite direction. The current density is uniformly distributed within each conductor. a) Find expressions for the magnetic field (B-field) in three regions: i) within the inner conductor ii) in the space between the conductors iii) outside the outer conductor. b) Draw a graph of B vrsus the cylindrical radius...
A coaxial cable consists of an internal solid cylindrical conductor of radius a and a cylindrical...
A coaxial cable consists of an internal solid cylindrical conductor of radius a and a cylindrical conductive thin shell of radius b separated by a dielectric of permittivity e.Assuming the length of the cable as infinite and that it carries a linear electric charge of qlcoulombs/meter, find the following:1. The electric field E for a ≤p≤b2. The voltage difference between the two conductor surfaces. 3. Since the maximum value of the electric field occurs at the surface p = a,...
An infinitely long straight wire is uniformly charged with a
positive linear charge density +?. It is surrounded by an
insulating hollow cylinder (also infinitely long) of inner radius R
and outer radius 2R. The hollow cylinder has a uniform charge
density ?.
(a) Determine the value of ? if the electric field vanishes at
every point outside the cylinder (r > 2R).
(b) Determine the electric field in the region 0 < r <
R.
(c) Determine the electric...
18. A infinitely long cable consists of a solid cylindrical inner conductor of radius a, surrounded by a concentric cylindrical conducting shell of inner radius b and outer radius c. The inner conductor has a non-uniform current density (r) = ar in the z direction shown. a is a positive constant with units A-m'. The outer conductor has a uniform current density: Jr) = -B (in negative z). B has the same unit as a. The conductors carry equal and...
An infinitely long, thin wire has a known current of 2i, which flows in the negative x-direction. It is surrounded by an infinitely long, hollow cylindrical wire so the wires have a common axis. The hollow wire has inner radius A and outer radius B. A known current i, which is uniformly spread over the hollow wire, flows in the positive x-direction in the hollow cylindrical wire. Cross-Section View A 2i i 0 +x 2 Z B +x What is...
An infinitely long, thin wire has a known current of 2i, which flows in the negative x-direction. It is surrounded by an infinitely long, hollow cylindrical wire so the wires have a common axis. The hollow wire has inner radius A and outer radius B. A known current i, which is uniformly spread over the hollow wire, flows in the positive x-direction in the hollow cylindrical wire. Cross-Section View A 21 0 +x 2 Z B 210. +x ♡ What...
4. Consider an infinitely long, thin, uniformly charged wire length. Symmetry dictates that the electric field in cylindrical coordinates will have only an r component (i.e. no θ or k components). Use the superposition principle to show that the electric field in cylindrical coordinates is with charge density λ per unit (4.63) 2 Hint: You will find the integral useful 2 )3/2 5. Find an expression for the voltage field around the wire in question 4.
4. Consider an infinitely...
6. (3 points) A coaxial cable consists of a solid inner conductor of radius Ri, surrounded by a concentric cylindrical tube of inner radius R2 and outer radius Rs (called the shield) as shown in Figure 8. The conductors carry equal and opposite currents, I, distributed uniformly across their cross sections. Determine the magnetic field at a distance r from the axis for: (a) r< Ri (b) Ri < R2 Page 2 (c) R2<r<Rs (d) R3 (e) Plot the magnitude...
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