A coaxial cable, commonly used in telecommunications, is a cylindrical capacitor. A given cable section has...

A coaxial cable, commonly used in telecommunications, is a cylindrical capacitor. A given cable section has a capacitance per unit length c0 [uF / m], length L0 [m] and relative electrical permittivity k0 []. It is decided to modify the cable in such a way that the external radius doubles, all other dimensions and materials remain the same. Calculate the new value of the capacitance per unit length.

Calculate the answer algebraically and evaluate for the following values. Write your answer in the box indicated with two decimal places in units of nF / m:

c0 = 50 uF / m

k = 3.2

ε0 = 8.85x10-12 C / (Vm)

Expert Solution

genius_generous answered 2 years ago

) A coaxial cable consists of a cylinder of radius ? surrounding by a thin cylindrical...

) A coaxial cable consists of a cylinder of radius ? surrounding by a thin cylindrical shell of radius 2?. Suppose the cable is along the ?-axis. The current density in inner cylinder is ? ⃗= (?0 + ??)?̂, where ?0 > 0 and ? > 0 are constant. The current in the outer shell, ?? ,is downward (−? direction). a) Find the magnetic field in regions 0 < ? < ?,? < ? < 2? and 2? < ?....

A coaxial cable consists of a long cylindrical copper wire of radius r1 surrounded by a...

A coaxial cable consists of a long cylindrical copper wire of radius r1 surrounded by a cylindrical insulating shell of outer radius r2 . A final conducting cylindrical shell of outer radius r3 surrounds the insulating shell. The wire and conducting shell carry equal but opposite currents I uniformly distributed over their volumes. What is the current density j(r) for all r? Find formulas for the magnetic field in each of the regions.

A very long coaxial cable consists of a solid cylindrical inner conductor of radius 3.8mm ,...

A very long coaxial cable consists of a solid cylindrical inner conductor of radius 3.8mm , surrounded by an outer cylindrical conductor with inner radius 7mm , and outer radius 9.3mm . The region between the two conductors is filled with a waxlike insulating material to keep the conductors from touching each other. The inner conductor carries a current 4.65A , into the page, while the outer conductor carries a current 4.6A , out of the page. Part A Use...

Consider a cylindrical coaxial cable. The center conductor is solid with radius R, while the outer...

Consider a cylindrical coaxial cable. The center conductor is solid with radius R, while the outer conductor is hollow with inner radius a and outer radius b, Both conductors have the same total current I (of uniform current density), but moving in the opposite direction of each other. Find the magnitude of the magnetic field as a function of r (where r=0 at the central axis) in the interval a is less than or equal to r is less than...

his animation shows a coaxial capacitor with cylindrical geometry: a very long cylinder (extending into and...

his animation shows a coaxial capacitor with cylindrical geometry: a very long cylinder (extending into and out of the page) in the center surrounded by a very long cylindrical shell (position is given in centimeters, electric field strength is given in newtons/coulomb, and electric potential is given in volts). The outside shell is grounded, while the inside shell is at 10 V. You can click-drag to measure the voltage at any position a cylindrical coaxial capacitor of length L is...

Consider an infinitely long, straight coaxial cable consisting of a homogeneous cylindrical center conductor with radius...

Consider an infinitely long, straight coaxial cable consisting of a homogeneous cylindrical center conductor with radius a and a surrounding conductive tube (shield) with inner radius b. The space between the center conductor and the screen is filled with a dielectric with er (epsilon r) = 1. In the inner conductor, a direct current I is distributed evenly over the cross section. In the outer conductor there is a corresponding return current. On the surface of the inner conductor there...

A short section of coaxial cable consists of a line current along the z-axis from z...

A short section of coaxial cable consists of a line current along the z-axis from z = -L to z = L carrying current ?0?̂ surrounded by a hollow cylindrical shell (centered on the z-axis, top at z = L , bottom at z = -L) carrying a surface current ?⃗⃗ = ?0 (−?̂). Radius R a. Find an expression for the magnetic field at an arbitrary point (x, y, z) b. Draw a qualitative graph of the magnetic field...

Coaxial cable. The inner cable has a radius R1 and carries D, a current per cross...

Coaxial cable. The inner cable has a radius R1 and carries D, a current per cross sectional area. The outer cable is a sheath cable, very thin, and carries an equal total current but in the opposite direction at a radius R2. There is a spacer between the two cables and a rubber coating on the outside for safety purposes. (Give answers in terms of R1, R2, D, and universal constants, plus r only when specified) a) Determine the total...

A coaxial cable is made of two conductors, the inner one has radius a and the...

A coaxial cable is made of two conductors, the inner one has radius a and the outer radius is b, both conductors are seperated by a dielectric material with relative permitivity εr and conductivity σ , what is the conductance per unit length of this insulating material. Show all steps you followed to obtain the final expression.

A 57.40-pF cylindrical capacitor carries a charge of 1.740 µC. The capacitor has a length of...

A 57.40-pF cylindrical capacitor carries a charge of 1.740 µC. The capacitor has a length of 1.400 ✕ 10−3 m. (a) What is the potential difference across the capacitor? V (b) If the radial separation between the two cylinders is 6.380 ✕ 10−4 m, what are the inner and outer radii of the cylindrical conductors? (Use 8.854 ✕ 10−12 C2/(N · m2) for the permittivity of free space. Give your answers to at least four decimal places.) rin = m...

Question