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(a) Sketch the set V given in spherical coordinates. Also include a sketch of a vertical cross- section passing through the origin. 20 (b) Calculate the volume of V. (a) Sketch the set V given i...
(a) Sketch the set V given in spherical coordinates. Also include a sketch of a vertical cross- section passing through the origin 2θ (b) Calculate the volume of V. (a) Sketch the set V given in...
(a) Sketch the set V given in spherical coordinates. Also include a sketch of a vertical cross- section passing through the origin 2θ (b) Calculate the volume of V.
(a) Sketch the set V given in spherical coordinates. Also include a sketch of a vertical cross- section passing through the origin 2θ (b) Calculate the volume of V.
1. Use cylindrical coordinates to SET UP the integral for the volume of the portion of...
1. Use cylindrical coordinates to SET UP the integral for the volume of the portion of the unit ball, 22 +232 + x2 < 1, above the plane z = 12 2. (a) Write in spherical coordinates the equations of the following surfaces: (i) x2 + y2 + x2 = 4 (ii) z = 3x2 + 3y2 (b) SET UP the integral in spherical coordinates for the volume of the solid inside the surface 22 + y2 + x2 =...
A charged particle is held at the center of two concentric conducting spherical shells. Figure (a) shows a cross section. Figure (b) gives the net flux Φ through a Gaussian sphere centered on the particle
A charged particle is held at the center of two concentric conducting spherical shells. Figure (a) shows a cross section. Figure (b) gives the net flux Φ through a Gaussian sphere centered on the particle, as a function of the radius r of the sphere. The scale of the vertical axis is set by Φs = 5.5 × 105 N·m2/c. what are (a) the charge of the central particle and the net charges of (b) shell A and (c) shell...
pleasee, you can do any solution:( The beam, the cross section of which is given in...
pleasee, you can do any solution:(
The beam, the cross section of which is given in the figure, consists of 25 mm thick boards. The slip safety stress for nails is given as tem= 100MPa. The diameter of the nails is 5 mm and the gap between the nails along the beam axis is 200 mm · (30P) according to this 50 200 a) Calculate the intensity of the maximum V shear force that can be applied to the cross...
(b) Calculate the percentage transmission for: (i) 20 keV X-rays passing through: 15 mm soft tissue,...
(b) Calculate the percentage transmission for: (i) 20 keV X-rays passing through: 15 mm soft tissue, 15 mm bone and 15 mm soft tissue 100 keV X-rats passing through: 150 mm soft tissue Compare the answers to (i) and (i) (i) (ii) The data required is given on the Figure 1 (40 marks) 100 lodine Calcium Water 10 O.14 10 20 30 40 50 60 70 80 90 100 110 Energy (keV) Rajah 1 Figure 1 Mass Attenuation Coefficient (cm1g)...
Q4 only: Question 3. Consider the region of R3 given by V is bounded by three surfaces. Si is a disc of radius 1 in the plane z -0. S3 is a disc of radius 2 in the plane z 3 and a) Make a clear sketc...
Q4 only:
Question 3. Consider the region of R3 given by V is bounded by three surfaces. Si is a disc of radius 1 in the plane z -0. S3 is a disc of radius 2 in the plane z 3 and a) Make a clear sketch of V. (Hint: You could consider the cross-section of S2 with y-0, and then use the circular symmetry. (b) Express V in cylindrical coordinates. (c) Calculate the volume of V, working in cylindrical...
20. The figure below shows a cross section through a very large nonconducting slab of thickness...
20. The figure below shows a cross section through a very large nonconducting slab of thickness d and uniform volume charge density p > 0. The origin of the x axis is at the centre of the slab. (a) Use symmetry considerations to show that the electric field inside and outside the slab has the form E = E(x) i, where E(-x) = -E(x). (b) Use Gauss's law to find the electric field E produced by the slab as a...
1. A point-charge q moving at velocity valong the z-axis is passing through the coordinate origin (a) Calculate aEa t in the Coulomb approximation on the +z-axis ahead of the charge [qy2π4 (b) Use th...
1. A point-charge q moving at velocity valong the z-axis is passing through the coordinate origin (a) Calculate aEa t in the Coulomb approximation on the +z-axis ahead of the charge [qy2π4 (b) Use the Biot-Savart law to calculate Βφ off-axis near the point in (a), ati distance r« z from it (use (c) Check (i) that VxB has the expected value (predicted by the relevant Maxwell's equation) in the cylindrical coordinates)o1. neighborhood of the point in question, and (ii)...
#1 and #3 I) )A solid insulating sphere of radius a carries a net positive charge density 3p uniformly distributed throughout its volume. A conducting spherical shell of inner radius 2a and outer...
#1 and #3
I) )A solid insulating sphere of radius a carries a net positive charge density 3p uniformly distributed throughout its volume. A conducting spherical shell of inner radius 2a and outer radius 3a is concentric with the solid sphere and carries a net charge density-22 Using Gauss's law, find the electric field everywhere. Sketch the electric field 2) "A) The current density in a cylindrical wire of radius R meters is uniform across a cross section of the...
please see instruction in pictures 3) Calculations: to be completed on one side of engineering paper must be neat and must include: a) Drawn to scale, a cross section of your member- inclu...
please see instruction in pictures
3) Calculations: to be completed on one side of engineering paper must be neat and must include: a) Drawn to scale, a cross section of your member- include all dimensions for your case Hand calculations of Area, A, (in), Location of the Centroid, ỹ, (X-X), Moment of inertia, l (in*), Section Modulus, S Using bottom center of the given cross section as an origin, list all the coordinates in tabular form for the critical intersections...
(a) Sketch the set V given in spherical coordinates. Also include a sketch of a vertical cross- section passing through the origin 2θ (b) Calculate the volume of V.
(a) Sketch the set V given in spherical coordinates. Also include a sketch of a vertical cross- section passing through the origin 2θ (b) Calculate the volume of V.
1. Use cylindrical coordinates to SET UP the integral for the volume of the portion of the unit ball, 22 +232 + x2 < 1, above the plane z = 12 2. (a) Write in spherical coordinates the equations of the following surfaces: (i) x2 + y2 + x2 = 4 (ii) z = 3x2 + 3y2 (b) SET UP the integral in spherical coordinates for the volume of the solid inside the surface 22 + y2 + x2 =...
pleasee, you can do any solution:(
The beam, the cross section of which is given in the figure, consists of 25 mm thick boards. The slip safety stress for nails is given as tem= 100MPa. The diameter of the nails is 5 mm and the gap between the nails along the beam axis is 200 mm · (30P) according to this 50 200 a) Calculate the intensity of the maximum V shear force that can be applied to the cross...
(b) Calculate the percentage transmission for: (i) 20 keV X-rays passing through: 15 mm soft tissue, 15 mm bone and 15 mm soft tissue 100 keV X-rats passing through: 150 mm soft tissue Compare the answers to (i) and (i) (i) (ii) The data required is given on the Figure 1 (40 marks) 100 lodine Calcium Water 10 O.14 10 20 30 40 50 60 70 80 90 100 110 Energy (keV) Rajah 1 Figure 1 Mass Attenuation Coefficient (cm1g)...
Q4 only:
Question 3. Consider the region of R3 given by V is bounded by three surfaces. Si is a disc of radius 1 in the plane z -0. S3 is a disc of radius 2 in the plane z 3 and a) Make a clear sketch of V. (Hint: You could consider the cross-section of S2 with y-0, and then use the circular symmetry. (b) Express V in cylindrical coordinates. (c) Calculate the volume of V, working in cylindrical...
20. The figure below shows a cross section through a very large nonconducting slab of thickness d and uniform volume charge density p > 0. The origin of the x axis is at the centre of the slab. (a) Use symmetry considerations to show that the electric field inside and outside the slab has the form E = E(x) i, where E(-x) = -E(x). (b) Use Gauss's law to find the electric field E produced by the slab as a...
1. A point-charge q moving at velocity valong the z-axis is passing through the coordinate origin (a) Calculate aEa t in the Coulomb approximation on the +z-axis ahead of the charge [qy2π4 (b) Use the Biot-Savart law to calculate Βφ off-axis near the point in (a), ati distance r« z from it (use (c) Check (i) that VxB has the expected value (predicted by the relevant Maxwell's equation) in the cylindrical coordinates)o1. neighborhood of the point in question, and (ii)...
#1 and #3
I) )A solid insulating sphere of radius a carries a net positive charge density 3p uniformly distributed throughout its volume. A conducting spherical shell of inner radius 2a and outer radius 3a is concentric with the solid sphere and carries a net charge density-22 Using Gauss's law, find the electric field everywhere. Sketch the electric field 2) "A) The current density in a cylindrical wire of radius R meters is uniform across a cross section of the...
please see instruction in pictures
3) Calculations: to be completed on one side of engineering paper must be neat and must include: a) Drawn to scale, a cross section of your member- include all dimensions for your case Hand calculations of Area, A, (in), Location of the Centroid, ỹ, (X-X), Moment of inertia, l (in*), Section Modulus, S Using bottom center of the given cross section as an origin, list all the coordinates in tabular form for the critical intersections...
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