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1. (28 Points) A long current carrying pipe consists of two conducting layers. The first layer...
4. (25 points) A hollow conducting pipe has an inner radius of 2a/5 and an outer...
4. (25 points) A hollow conducting pipe has an inner radius of 2a/5 and an outer radius of a. The cross section is as shown below. It carries a current of magnitude Iwith uniform current density within the conductor material. Using Ampere's Law, find the magnetic field magnitude in each region as a function of radius (in the cavity contained within the pipe, within the pipe itself, and outside the pipe). Sketch a graph of the magnetic field magnitude as...
Cross-sectional View (current into page) A section of a long conducting cylinder with inner radiu...
Cross-sectional View (current into page) A section of a long conducting cylinder with inner radius a and outer radius b carries a current lo that has a uniform current density, as shown in the figure above. (a) Using Ampère's law, derive an expression for the magnitude of the magnetic field in the following regions as a function of the distance r from the central axis. t. r<a ii. a<r<b (b) On the cross-sectional view in the diagram above, indicate the...
4. (12 points) A coaxial cable consists of a central conducting wire of radius a and...
4. (12 points) A coaxial cable consists of a central conducting wire of radius a and a surrounding conducting cylindrical shell of inner radius b and outer radius c. Suppose the central wire carries a current I and the outer shell carries a uniform current 21 in the same direction. Use Ampere's Law to find the magnitude of the magnetic field (a) (3 points) in the region between the wire and outer shell a <r <b, (b) (6 points) inside...
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...
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 nonconducting sphere is made of two layers. The innermost section has a radius of 6.0...
A nonconducting sphere is made of two layers. The innermost section has a radius of 6.0 cm and a uniform charge density of −5.0C/m3. The outer layer has a uniform charge density of +8.0C/m3 and extends from an inner radius of 6.0 cm to an outer radius of 12.0 cm. Part A Determine the electric field for 0<r<6.0cm. Part B Determine the electric field for 6.0cm. Part C Determine the electric field for 12.0cm<r<50.0cm.
As shown in the figure, a long, hollow, conducting cylinder of inner radius a and outer...
As shown in the figure, a long, hollow, conducting cylinder of
inner radius a and outer radius b carries a
current that is flowing out of the page. Suppose that a =
4.13 cm, b = 7.83 cm, and the current i = 273 mA,
uniformly distributed over the cylinder wall (between a
and b). Find the magnitude of the magnetic field at each
of the following distances r from the center of the
cylinder:
As shown in the figure,...
Problem 4 (20 points): A long, solid conducting cylinder of radius R has a current density within...
Problem 4 (20 points): A long, solid conducting cylinder of radius R has a current density within it described by: (r)-C( ) for r< R where C is a constant to be determined. The total current running through the whole cylinder is I. a) Calculate an expression for the constant C, given that the total current is I. (Hint: the current density is not uniform.) b) Why can Ampere's law be used here, and what Amperian loop is appropriate? c)...
Consider a pipe consisting of two layers: Consider a pipe consisting of two layers: • an...
Consider a pipe consisting of two layers:
Consider a pipe consisting of two layers: • an inner layer of AISI 1010 steel with thickness 2 cm, and • an outer layer of insulation (k = 0.034 W/(m · K)) with thickness 4 cm The pipe's contents keep the inner surface at a constant temperature of 120 °C, while the outside experiences convection with overall convection coefficient h 30 W/(m²K) to the surroundings at T = 25°C. The pipe's inner diameter...
Two circular current-carrying loops of wire are shown in the drawing. The inner loop has a...
Two circular current-carrying loops of wire are shown in the drawing. The inner loop has a radius of R0 and carries a current I0, while the outer loop has a radius of 2R0 and carries a current of 4I0. The currents are in opposite directions. If R0 = 0.20 m and I0 = 2.3 A, determine the magnitude and direction of the net magnetic field at the center of the two loops.
4. (25 points) A hollow conducting pipe has an inner radius of 2a/5 and an outer radius of a. The cross section is as shown below. It carries a current of magnitude Iwith uniform current density within the conductor material. Using Ampere's Law, find the magnetic field magnitude in each region as a function of radius (in the cavity contained within the pipe, within the pipe itself, and outside the pipe). Sketch a graph of the magnetic field magnitude as...
Cross-sectional View (current into page) A section of a long conducting cylinder with inner radius a and outer radius b carries a current lo that has a uniform current density, as shown in the figure above. (a) Using Ampère's law, derive an expression for the magnitude of the magnetic field in the following regions as a function of the distance r from the central axis. t. r<a ii. a<r<b (b) On the cross-sectional view in the diagram above, indicate the...
4. (12 points) A coaxial cable consists of a central conducting wire of radius a and a surrounding conducting cylindrical shell of inner radius b and outer radius c. Suppose the central wire carries a current I and the outer shell carries a uniform current 21 in the same direction. Use Ampere's Law to find the magnitude of the magnetic field (a) (3 points) in the region between the wire and outer shell a <r <b, (b) (6 points) inside...
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...
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...
As shown in the figure, a long, hollow, conducting cylinder of
inner radius a and outer radius b carries a
current that is flowing out of the page. Suppose that a =
4.13 cm, b = 7.83 cm, and the current i = 273 mA,
uniformly distributed over the cylinder wall (between a
and b). Find the magnitude of the magnetic field at each
of the following distances r from the center of the
cylinder:
As shown in the figure,...
Problem 4 (20 points): A long, solid conducting cylinder of radius R has a current density within it described by: (r)-C( ) for r< R where C is a constant to be determined. The total current running through the whole cylinder is I. a) Calculate an expression for the constant C, given that the total current is I. (Hint: the current density is not uniform.) b) Why can Ampere's law be used here, and what Amperian loop is appropriate? c)...
Consider a pipe consisting of two layers:
Consider a pipe consisting of two layers: • an inner layer of AISI 1010 steel with thickness 2 cm, and • an outer layer of insulation (k = 0.034 W/(m · K)) with thickness 4 cm The pipe's contents keep the inner surface at a constant temperature of 120 °C, while the outside experiences convection with overall convection coefficient h 30 W/(m²K) to the surroundings at T = 25°C. The pipe's inner diameter...
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