For the section of a sphere described by 1 ≤ ? ≤ 3, 90° ≤ ?...
For the section of a sphere described by 1 ≤ ? ≤ 3, 90° ≤ ? ≤ 180°, 0° ≤ ? ≤ 60° , by expressing the respective integrations, find,
(i) The total surface area of the spherical section
(ii) The volume of the spherical section
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A section of a sphere is described by 0 R 2. O θε 90%, and 30。sO...
A section of a sphere is described by 0 R 2. O θε 90%, and 30。sO 90%. Find the following: (a) The surface area of the spherical section. (b) The enclosed volume. Also sketch the outline of the section
In 2D, a sphere can be described by 2+sr. In 3D, a sphere can be described...
In 2D, a sphere can be described by 2+sr. In 3D, a sphere can be described by r2 + y2 + .2-r*. We can talk about a sphere in n-dimensions by defining it like++2 Using what we know about multivariable calculus, believe it or not, it is relatively easy to calculate the volume of an n -dimensional sphere. It turns out that the volume of a 5th dimensional sphere of radius 1 will be a maximum, and then the volume...
H8 Hard Sphere Scattering The dlifferential cross-section in the CM frame is given in terms of th...
H8 Hard Sphere Scattering The dlifferential cross-section in the CM frame is given in terms of the impact parameter b and the CM scattering angle 0" by: do b db sin () Two identical hard spheres of mass m and radius R scatter off each other. Find the differential cross-section in the CM frame, σ(F). (ii) Show that the relationship between the LAB and CMI scattering angles θ and for identical spheres can be written in the form: (ii) Use...
There is a small sphere with volume, V, surface area, As, and specific heat, c. The sphere was in...
There is a small sphere with volume, V, surface area, As, and specific heat, c. The sphere was initially was at T, and was placed in liquid with temperature To and heat transfer coefficient h. Show the governing equation and temperature as a function of time when (i) Ti > To and (ii) Ti < T. You can use the lumped capacitance analysis. (20 pt) 3.
There is a small sphere with volume, V, surface area, As, and specific heat,...
For the described solid S, write the triple integral f(x,y, z)dV as an iterated integral in (i) r...
For the described solid S, write the triple integral f(x,y, z)dV as an iterated integral in (i) rectangular coordinates (x,y, z); (ii) cylindrical coordinates (r, 0, 2); (iii) spherical coordinates (p, φ,0). a. Inside the sphere 2 +3+224 and above the conezV b. Inside the sphere x2 + y2 + 22-12 and above the paraboloid z 2 2 + y2. c. Inside the sphere 2,2 + y2 + z2-2 and above the surface z-(z2 + y2)1/4 d. Inside the sphere...
Let us denote the volume and the surface area of an n-dimensional sphere of adius R as V(OR)-VR a...
We were unable to transcribe this imageLet us denote the volume and the surface area of an n-dimensional sphere of adius R as V(OR)-VR and S(R)-S.),respectively (a) Find the relation between V(0) and S 1) (b) Calculate the Gaussian integral 3. (c) Calculate the same integral in spherical coordinates in terms of the gamma function re)-e'd (d) Obtain the closed forms of S,,(1) and V(1) (e) Calculate r5) and S.,0), p.(1) for n-1, 2, 3. (40 points)
Let us denote...
Cylinder In Sphere A cylinder has a volume of 4.2 cm^3 and a charge density of...
Cylinder In Sphere A cylinder has a volume of 4.2 cm^3 and a charge density of 3.5 μC/cm^3, and is enclosed in a spherical surface with a radius of 15.5 cm as shown in the figure. What is the total charge on the cylinder? What is the total electric flux through the surface of the sphere?
Consider a sphere of radius a with a uniform charge distribution over its volume, and a...
Consider a sphere of radius a with a uniform charge distribution over its volume, and a total charge of q_o. Use Gauss's Law to calculate the electric field outside the sphere, and then inside the sphere. Solve the general problem in r, recognizing that problem spherical symmetry. Draw a graph of the electric field the has the surface of the strength as a function of noting where if the surface of the sphere is (a). Some hints: the surface area...
18a) Find the flux through the whole surface of the sphere. b) Find the magnitude and...
18a) Find the flux through the whole surface of the sphere. b) Find the magnitude and direction of E at the surface.1 Now put the same charge at the center of a spherical shell- with twice the diameter. c) Find the magnityde and direction of E at the surface.1 d) Find the flux through the whole surface of the sphere.1 e) Why is the flux the same, even though E is weaker?1 18, A particle with charge of 12.0 μC...
Sphere 1 has surface area Ai and volume Vi and sphere 2 has surface area A2...
Sphere 1 has surface area Ai and volume Vi and sphere 2 has surface area A2 and volume V2. If the radius of sphere 2 is 1.84 times the radius of sphere 1, what is the ratio of the areas A2/A1? Tries 0/8 What is the ratio of the volumes V2/V1? Tries 0/8 Submit Answer Submit An Post Discussion Sen
A section of a sphere is described by 0 R 2. O θε 90%, and 30。sO 90%. Find the following: (a) The surface area of the spherical section. (b) The enclosed volume. Also sketch the outline of the section
In 2D, a sphere can be described by 2+sr. In 3D, a sphere can be described by r2 + y2 + .2-r*. We can talk about a sphere in n-dimensions by defining it like++2 Using what we know about multivariable calculus, believe it or not, it is relatively easy to calculate the volume of an n -dimensional sphere. It turns out that the volume of a 5th dimensional sphere of radius 1 will be a maximum, and then the volume...
H8 Hard Sphere Scattering The dlifferential cross-section in the CM frame is given in terms of the impact parameter b and the CM scattering angle 0" by: do b db sin () Two identical hard spheres of mass m and radius R scatter off each other. Find the differential cross-section in the CM frame, σ(F). (ii) Show that the relationship between the LAB and CMI scattering angles θ and for identical spheres can be written in the form: (ii) Use...
There is a small sphere with volume, V, surface area, As, and specific heat, c. The sphere was initially was at T, and was placed in liquid with temperature To and heat transfer coefficient h. Show the governing equation and temperature as a function of time when (i) Ti > To and (ii) Ti < T. You can use the lumped capacitance analysis. (20 pt) 3.
There is a small sphere with volume, V, surface area, As, and specific heat,...
For the described solid S, write the triple integral f(x,y, z)dV as an iterated integral in (i) rectangular coordinates (x,y, z); (ii) cylindrical coordinates (r, 0, 2); (iii) spherical coordinates (p, φ,0). a. Inside the sphere 2 +3+224 and above the conezV b. Inside the sphere x2 + y2 + 22-12 and above the paraboloid z 2 2 + y2. c. Inside the sphere 2,2 + y2 + z2-2 and above the surface z-(z2 + y2)1/4 d. Inside the sphere...
We were unable to transcribe this imageLet us denote the volume and the surface area of an n-dimensional sphere of adius R as V(OR)-VR and S(R)-S.),respectively (a) Find the relation between V(0) and S 1) (b) Calculate the Gaussian integral 3. (c) Calculate the same integral in spherical coordinates in terms of the gamma function re)-e'd (d) Obtain the closed forms of S,,(1) and V(1) (e) Calculate r5) and S.,0), p.(1) for n-1, 2, 3. (40 points)
Let us denote...
Consider a sphere of radius a with a uniform charge distribution over its volume, and a total charge of q_o. Use Gauss's Law to calculate the electric field outside the sphere, and then inside the sphere. Solve the general problem in r, recognizing that problem spherical symmetry. Draw a graph of the electric field the has the surface of the strength as a function of noting where if the surface of the sphere is (a). Some hints: the surface area...
18a) Find the flux through the whole surface of the sphere. b) Find the magnitude and direction of E at the surface.1 Now put the same charge at the center of a spherical shell- with twice the diameter. c) Find the magnityde and direction of E at the surface.1 d) Find the flux through the whole surface of the sphere.1 e) Why is the flux the same, even though E is weaker?1 18, A particle with charge of 12.0 μC...
Sphere 1 has surface area Ai and volume Vi and sphere 2 has surface area A2 and volume V2. If the radius of sphere 2 is 1.84 times the radius of sphere 1, what is the ratio of the areas A2/A1? Tries 0/8 What is the ratio of the volumes V2/V1? Tries 0/8 Submit Answer Submit An Post Discussion Sen
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