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Problem 4. (4 points) The radial resistance of a coaxial...
Q9) A coaxial cable of length L-10m, has inner and outerradii of a-1 mm and b-3 mm. The region a p<b is a dielectric with Ep-2 and conductivity σ-0.01 S/m. Let V-10 V at ρ-a and V-0 V at ρ-b,...
Q9) A coaxial cable of length L-10m, has inner and outerradii of a-1 mm and b-3 mm. The region a p<b is a dielectric with Ep-2 and conductivity σ-0.01 S/m. Let V-10 V at ρ-a and V-0 V at ρ-b, find i. Eand Vin the region a <ρ<b. ii. The capacitance per unit length. iii. ρ,atpra. iv. The stored energy per unit length. v. The resistance between the inner and outer conductors. vi. The leakage current (the current between the...
Question 1: Calculate the self-inductance of: (a) 5 cm of coaxial cable with a- 0.4 mm...
Question 1: Calculate the self-inductance of: (a) 5 cm of coaxial cable with a- 0.4 mm and b-2 mm, filled with material for which Hr-30; (b) a solenoid having 100 turns about a cylindrical core of4 cm radius in which μ.-50 for 0 < ρ < 1 cm and μ,-1 for l < ρ < 2 cm; the length of the solenoid is 25 cm. (5+5-10 marks)
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 cable of length 1 = 4m consists of a solid cylindrical conductor surrounded by...
A coaxial cable of length 1 = 4m consists of a solid cylindrical conductor surrounded by a cylindrical conducting shell. The inner conductor has a radius ry = 2mm and carries a charge Q, while the surrounding shell has a radius ra = 8mm and carries a charge -Q. Assume that Q = +8 x 10-8C and that air fills the gap between the conductors. (a) What is the capacitance of this cable? (b) What is the magnitude of the...
2. Leakage Resistance of a Coax Cable The leakage resistivity of a coax cable's insulation is...
2. Leakage Resistance of a Coax Cable The leakage resistivity of a coax cable's insulation is measured as follows. A known potential difference V is applied across the two conductors in a length L of the cable; the leakage current I that flows between them (through the insulation) is measured; and the resistivity is calculated from the voltage and current. The inner conductor has radius a and the outer conductor has inner radius b. The insulator fills the space between...
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...
2. A modified coaxial cable consists of a solid cylinder (radius 'a') with a uniform current...
2. A modified coaxial cable consists of a solid cylinder (radius 'a') with a uniform current density and a concentric cylindrical conducting thin shell (radius 'b'). The outer and inner current have an equal magnitude, but are opposite in direction. Io (along outside) (along the axis) (off-axis view) In terms of radial distance 'r', and the relevant parameters in the diagram above, A) Derive an expression for the magnetic field inside the solid cylinder (r <a) B) Derive an expression...
A.) We'll start with a very long coaxial cable that has two parts. There's a conducting...
A.) We'll start with a very long coaxial cable that has two parts. There's a conducting cylindrical inner wire of radius a, and a conducting cylindrical sheath around that with radius b. The space in between (a<r<b) is empty. Let the inner conductor have some linear charge density lambda along its length. Derive an expression for the magnitude of the electric field between the inner and outer conductors as a function of r. B.) Consider the same geometry as the...
6. 10 points A coaxial cable of length L consists of one cylinder of radius a...
6. 10 points A coaxial cable of length L consists of one cylinder of radius a and an- other of radius 2a. The space between the two cylinders is filled with a medium of conductivity o. The inner cylinder is held at Vo and the outer cylinder is grounded (see figure below). a) Using Poisson's equation, compute the electric field and electric potential inside the medium. (4 pts) b) Compute the resistance between the two cylinders. (6 pts) V=VO 2a...
2. A coaxial capacitor has radii a = 4 cm and b = 12 cm. If...
2. A coaxial capacitor has radii a = 4 cm and b = 12 cm. If the space between the plates is filled with an inhomogeneous dielectric with εr = (ρ + 2.5)/ρ, where ρ is in meters, find the capacitance per meter of the capacitor.
Q9) A coaxial cable of length L-10m, has inner and outerradii of a-1 mm and b-3 mm. The region a p<b is a dielectric with Ep-2 and conductivity σ-0.01 S/m. Let V-10 V at ρ-a and V-0 V at ρ-b, find i. Eand Vin the region a <ρ<b. ii. The capacitance per unit length. iii. ρ,atpra. iv. The stored energy per unit length. v. The resistance between the inner and outer conductors. vi. The leakage current (the current between the...
Question 1: Calculate the self-inductance of: (a) 5 cm of coaxial cable with a- 0.4 mm and b-2 mm, filled with material for which Hr-30; (b) a solenoid having 100 turns about a cylindrical core of4 cm radius in which μ.-50 for 0 < ρ < 1 cm and μ,-1 for l < ρ < 2 cm; the length of the solenoid is 25 cm. (5+5-10 marks)
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 cable of length 1 = 4m consists of a solid cylindrical conductor surrounded by a cylindrical conducting shell. The inner conductor has a radius ry = 2mm and carries a charge Q, while the surrounding shell has a radius ra = 8mm and carries a charge -Q. Assume that Q = +8 x 10-8C and that air fills the gap between the conductors. (a) What is the capacitance of this cable? (b) What is the magnitude of the...
2. Leakage Resistance of a Coax Cable The leakage resistivity of a coax cable's insulation is measured as follows. A known potential difference V is applied across the two conductors in a length L of the cable; the leakage current I that flows between them (through the insulation) is measured; and the resistivity is calculated from the voltage and current. The inner conductor has radius a and the outer conductor has inner radius b. The insulator fills the space between...
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...
2. A modified coaxial cable consists of a solid cylinder (radius 'a') with a uniform current density and a concentric cylindrical conducting thin shell (radius 'b'). The outer and inner current have an equal magnitude, but are opposite in direction. Io (along outside) (along the axis) (off-axis view) In terms of radial distance 'r', and the relevant parameters in the diagram above, A) Derive an expression for the magnetic field inside the solid cylinder (r <a) B) Derive an expression...
6. 10 points A coaxial cable of length L consists of one cylinder of radius a and an- other of radius 2a. The space between the two cylinders is filled with a medium of conductivity o. The inner cylinder is held at Vo and the outer cylinder is grounded (see figure below). a) Using Poisson's equation, compute the electric field and electric potential inside the medium. (4 pts) b) Compute the resistance between the two cylinders. (6 pts) V=VO 2a...
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