Solve Laplace’s equation in cylindrical coordinates to obtain the potential function inside of a ...
Solve Laplace’s equation in cylindrical coordinates to obtain the potential function inside of a coaxial cable, having inner radius a and outer radius b. The cable is filled with a dielectric having a relative permittivity εr. The potential on the inner conductor is V0 volts, while the outer conductor (the shield) has a potential of zero volts. Note that the potential should only be a function of the radial distance ρ.
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Solve Laplace’s equation in cylindrical coordinates to obtain the potential function inside of a ...
4. (12 points) Ampere's law in cylindrical coordinates (p,p,z.) An infinitely long coaxial cable is given in the fi...
4. (12 points) Ampere's law in cylindrical coordinates (p,p,z.) An infinitely long coaxial cable is given in the figure below. The inner conductor has a radius of R1 = 1.00cm. The outer conductor has a radius R2 = 2.00cm and has negligible thickness. The inner conductor has a current density given by J 2.00A p (TR1) flowing out of the page (positive z direction), where ρ is the radial direction. The outer conductor has a current 1 of 1.00 Amperes...
A coaxial capacitor (cylindrical shape) is filled with two coaxial dielectric lasers. The relative permittivity of...
A coaxial capacitor (cylindrical shape) is filled with two coaxial dielectric lasers. The relative permittivity of the layer near the inner electrode of the capacitor is epsilon_r|, and that of the other laser is epsilon_r2. The radius of the inner electrode is a, the radius of the boundary surface between the layers is b, and the inner radius of the outer electrode is c. Calculate the capacitance per unit length of the cable. If the voltage between the inner and...
P25.5. Compare the loss in the inner conductor and outer conductor of a coaxial cable at 1 MHz. A...
P25.5. Compare the loss in the inner conductor and outer conductor of a coaxial cable at 1 MHz. Assume the conductors are made of copper, that the cable is filled with a dielectric of permittivity er - 3, and that the dimensions are such that the inner conductor radiu:s a = 0.45 mm, and inner radius of the outer conductor b ae. The ratio of losses per unit length in the two conductors is: (a) 3.05. (b) 2.72. (c) 2.30....
5. Consider a very long coaxial cable, comprised of concentric cylindrical conductors with some insulating gap...
5. Consider a very long coaxial cable, comprised of concentric cylindrical conductors with some insulating gap between them. In particular, the inner solid cylindrical conductor has a radius, a, and carries a total, axial current, I. However, this current is not distributed uniformly along its circular cross section. In particular, the current density of this inner conductor is J(r) = Jovi where Jo is a positive constant that is to be determined and r labels the radial distance away from...
A coaxial line with cylindrical symmetry as shown in cross section by Figure A1-1. It is...
A coaxial line with cylindrical symmetry as shown in cross section by Figure A1-1. It is constructed from a solid inner conductor of radius a, a hollow outer conductor of internal radiusb and is filled with a dielectric having relative permittivity & 2b 2a Figure A1-1: Cross section of a coaxial transmission line (a) Draw lines of electric and magnetic flux for a coaxial transmission line. (4 marks) (b) Use Gauss' Law and a relationship between electric field and voltage...
Problem 2: Consider a coaxial cable with an inner conductor radius of a and outer conductor...
Problem 2: Consider a coaxial cable with an inner conductor radius of a and outer conductor radius of b. The region between the conductors is filled with a linear dielectric material that has a relative permittivity er (recall, ε = Er €0). A voltage V is applied to a length h of the cable, resulting in a free-charge of qf residing on the inner conductor and -9f residing on the outer conductor. Part a Determine the D, E, and P...
The Baltic cable connects the power grids of Germany and Sweden beneath the Baltic sea. Assume th...
The Baltic cable connects the power grids of Germany and Sweden
beneath the Baltic sea. Assume the cross section of the cable looks
as in the figure below. The coaxial cable has a cylindrical inner
conductor, radius a and an outer conductor, radius b, with
polyethylene (relative dielectric constant of 2.5; high dielectric
breakdown strength) in between. The outer conductor is surrounded
by a waterproof insulator (not shown). Assume that each conductor
holds charge ±Q per unit length.
5. The...
3. A coaxial cable has the inner conductor with radius of 0.8 mm and the outher...
3. A coaxial cable has the inner conductor with radius of 0.8 mm and the outher conductor with inside radius of 3.00 mm and outside radius of 4.00mm. The space between the conductors is filled with material having 2.3 dielectric constant and 18.0x 106 V/m dielectric strength. Calculate the maximum potential difference this cable can withstand.
A coaxial cable, as shown in Figure 2, consists of an inner conductor of radius a,...
A coaxial cable, as shown in Figure 2, consists of an inner conductor of radius a, surrounded by an outer conductor of radius b, along the same axis. The space is filled with dielectric. The cable is connected to a power supply and it is deposited a charge of +Q uniformly along the length of the surface of the inner conductor and a charge - Q uniformly along the length of the inner surface of the outer conductor. No fields...
A cylindrical conductor of inner radius a and outer radius b carries a steady current I....
A cylindrical conductor of inner radius a and outer radius b
carries a steady current I. The current density in the conductor is
uniform. Find B? as a function of the radial distance from the
cylinder’s axis.
4. A cylindrical conductor of inner radius a and outer radius b carries a steady current I. The current density in the conductor is uniform. Find B as a function of the radial distance from the cylinder's axis. EN
4. (12 points) Ampere's law in cylindrical coordinates (p,p,z.) An infinitely long coaxial cable is given in the figure below. The inner conductor has a radius of R1 = 1.00cm. The outer conductor has a radius R2 = 2.00cm and has negligible thickness. The inner conductor has a current density given by J 2.00A p (TR1) flowing out of the page (positive z direction), where ρ is the radial direction. The outer conductor has a current 1 of 1.00 Amperes...
A coaxial capacitor (cylindrical shape) is filled with two coaxial dielectric lasers. The relative permittivity of the layer near the inner electrode of the capacitor is epsilon_r|, and that of the other laser is epsilon_r2. The radius of the inner electrode is a, the radius of the boundary surface between the layers is b, and the inner radius of the outer electrode is c. Calculate the capacitance per unit length of the cable. If the voltage between the inner and...
P25.5. Compare the loss in the inner conductor and outer conductor of a coaxial cable at 1 MHz. Assume the conductors are made of copper, that the cable is filled with a dielectric of permittivity er - 3, and that the dimensions are such that the inner conductor radiu:s a = 0.45 mm, and inner radius of the outer conductor b ae. The ratio of losses per unit length in the two conductors is: (a) 3.05. (b) 2.72. (c) 2.30....
5. Consider a very long coaxial cable, comprised of concentric cylindrical conductors with some insulating gap between them. In particular, the inner solid cylindrical conductor has a radius, a, and carries a total, axial current, I. However, this current is not distributed uniformly along its circular cross section. In particular, the current density of this inner conductor is J(r) = Jovi where Jo is a positive constant that is to be determined and r labels the radial distance away from...
A coaxial line with cylindrical symmetry as shown in cross section by Figure A1-1. It is constructed from a solid inner conductor of radius a, a hollow outer conductor of internal radiusb and is filled with a dielectric having relative permittivity & 2b 2a Figure A1-1: Cross section of a coaxial transmission line (a) Draw lines of electric and magnetic flux for a coaxial transmission line. (4 marks) (b) Use Gauss' Law and a relationship between electric field and voltage...
Problem 2: Consider a coaxial cable with an inner conductor radius of a and outer conductor radius of b. The region between the conductors is filled with a linear dielectric material that has a relative permittivity er (recall, ε = Er €0). A voltage V is applied to a length h of the cable, resulting in a free-charge of qf residing on the inner conductor and -9f residing on the outer conductor. Part a Determine the D, E, and P...
The Baltic cable connects the power grids of Germany and Sweden
beneath the Baltic sea. Assume the cross section of the cable looks
as in the figure below. The coaxial cable has a cylindrical inner
conductor, radius a and an outer conductor, radius b, with
polyethylene (relative dielectric constant of 2.5; high dielectric
breakdown strength) in between. The outer conductor is surrounded
by a waterproof insulator (not shown). Assume that each conductor
holds charge ±Q per unit length.
5. The...
3. A coaxial cable has the inner conductor with radius of 0.8 mm and the outher conductor with inside radius of 3.00 mm and outside radius of 4.00mm. The space between the conductors is filled with material having 2.3 dielectric constant and 18.0x 106 V/m dielectric strength. Calculate the maximum potential difference this cable can withstand.
A coaxial cable, as shown in Figure 2, consists of an inner conductor of radius a, surrounded by an outer conductor of radius b, along the same axis. The space is filled with dielectric. The cable is connected to a power supply and it is deposited a charge of +Q uniformly along the length of the surface of the inner conductor and a charge - Q uniformly along the length of the inner surface of the outer conductor. No fields...
A cylindrical conductor of inner radius a and outer radius b
carries a steady current I. The current density in the conductor is
uniform. Find B? as a function of the radial distance from the
cylinder’s axis.
4. A cylindrical conductor of inner radius a and outer radius b carries a steady current I. The current density in the conductor is uniform. Find B as a function of the radial distance from the cylinder's axis. EN
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