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Question gif a veckor field F is fangent to a mufice S at every point ofs...
(1 point) Compute the flux of the vector field F 3z2y2 zk through the surface S...
(1 point) Compute the flux of the vector field F 3z2y2 zk through the surface S which is the cone vz2 y2 z, with 0z R, oriented downward. (a) Parameterize the cone using cylindrical coordinates (write 0 as theta). (r,)cos(theta) (r, e)rsin(theta) witho KTR and 0 (b) With this parameterization, what is dA? dA = | <0,0,(m5/2)sin^2(theta» (c) Find the flux of F through S flux
8. At every point on the surface of a sphere of radius 0.4 m the electric...
8. At every point on the surface of a sphere of radius 0.4 m the electric field is radially outward, with a magnitude of 20N/C. What is the flux through the spherical surface? 9. The flux through an imaginary spherical sur- face is 12 Nm2/C (a) What can you conclude about the charge within this surface? (b) What can you conclude about the charge within the spherical surface if, in addition, the electric field is radial, with the same magnitude...
(1) Let F denote the inverse square vector field (axr, y, z) F= (Note that ||F...
(1) Let F denote the inverse square vector field (axr, y, z) F= (Note that ||F 1/r2.) The domain of F is R3\{(0, 0, 0)} where r = the chain rule (a) Verify that Hint: first show that then use (b) Show that div(F 0. (c) Suppose that S is a closed surface in R3 that does not enclose the origin. Show that the flux of F through S is zero. Hint: since the interior of S does not contain...
EXERCISE 1.73. Prove that every proper rigid motion, f, of R3 that fixes the origin is...
EXERCISE 1.73. Prove that every proper rigid motion, f, of R3 that fixes the origin is a rotation about some axis. HINT: Write LA, where A E O(3) with det(A) 1. Notice that A has a real eigenvalue A R, because its characteristic polmomial is cubic Let vi denote a corresponding unit-length is orthogonal, A eigenvector, and complete it to an orthonormal basis (vi, V2,Va) of R. Shou that the matriz representing f with respect to this basis has the...
(1 point) Compute the flux of the vector field F(x, y, z) = 3 + 2+...
(1 point) Compute the flux of the vector field F(x, y, z) = 3 + 2+ 2k through the rectangular region with corners at (1,1,0), (0,1,0), (0,0,2), and (1,0, 2) oriented in the positive Z-direction, as shown in the figure. 2.0 1.5 Flux = 0.0 12.0 11.5 2 1.0 0.5 0.0 2.94. god. og 9.500.00 [Enable Java to make this image interactive] (Drag to rotate) (1 point) Compute the flux of the vector field F(t, y, z) = 31 +23...
This Question: 2 pts 29 of 35 Given a two-dimensional vector field F and a smooth oriented curve C, what is the meaning...
This Question: 2 pts 29 of 35 Given a two-dimensional vector field F and a smooth oriented curve C, what is the meaning of the flux of F across C? Choose the correct answer below A. The flux of F across C is the sum of the components of F tangent to C at each point of C. B. The flux of F across C is the component of F tangent to C at a point P on C O...
5. Setup (but do not evaluate) one integral (of any type) to find the flux of vector field F through surface S, where S s the unit cube given by 0 < x < 1,0 < y 1.0 < z 1, 5. Set...
5. Setup (but do not evaluate) one integral (of any type) to find the flux of vector field F through surface S, where S s the unit cube given by 0 < x < 1,0 < y 1.0 < z 1,
5. Setup (but do not evaluate) one integral (of any type) to find the flux of vector field F through surface S, where S s the unit cube given by 0
a) A vector field F is called incompressible if div F = 0. Show that a vector field of the form F = <f(y,z),g(x,z),h(x,y)> is incompressible. b) Suppose that S is a closed surface (a boundary o...
a) A vector field F is called incompressible if div F = 0. Show
that a vector field of the form F = <f(y,z),g(x,z),h(x,y)> is
incompressible.
b) Suppose that S is a closed surface (a boundary of a solid in
three dimensional space) and that F is an incompressible vector
field. Show that the flux of F through S is 0.
c)Show that if f and g are defined on R3 and C is a closed curve
in R3 then...
(a) Use surface integral(s) to calculate the flux of the vector field or through the given surface.
(a) Use surface integral(s) to calculate the flux of the vector field or through the given surface. (b) Use the divergence theorem to calculate the flux of the vector field through the given surface. 4. F(x, y, z) =x2yi - 2yzj + x2y2k; S is the surface of the rectangular solid in the first octant bounded by the planes x= 1,y=2, and z=3. Show your work and give an exact answer.
A point-like charge of 5µC is located at the origin. Find the flux of electric field...
A point-like charge of 5µC is located at the origin. Find the
flux of electric field
passing through a window at
defined by
and
.
Please use spherical cordinates and explain how you go about
solving this problem. Thank you
(1 point) Compute the flux of the vector field F 3z2y2 zk through the surface S which is the cone vz2 y2 z, with 0z R, oriented downward. (a) Parameterize the cone using cylindrical coordinates (write 0 as theta). (r,)cos(theta) (r, e)rsin(theta) witho KTR and 0 (b) With this parameterization, what is dA? dA = | <0,0,(m5/2)sin^2(theta» (c) Find the flux of F through S flux
8. At every point on the surface of a sphere of radius 0.4 m the electric field is radially outward, with a magnitude of 20N/C. What is the flux through the spherical surface? 9. The flux through an imaginary spherical sur- face is 12 Nm2/C (a) What can you conclude about the charge within this surface? (b) What can you conclude about the charge within the spherical surface if, in addition, the electric field is radial, with the same magnitude...
(1) Let F denote the inverse square vector field (axr, y, z) F= (Note that ||F 1/r2.) The domain of F is R3\{(0, 0, 0)} where r = the chain rule (a) Verify that Hint: first show that then use (b) Show that div(F 0. (c) Suppose that S is a closed surface in R3 that does not enclose the origin. Show that the flux of F through S is zero. Hint: since the interior of S does not contain...
EXERCISE 1.73. Prove that every proper rigid motion, f, of R3 that fixes the origin is a rotation about some axis. HINT: Write LA, where A E O(3) with det(A) 1. Notice that A has a real eigenvalue A R, because its characteristic polmomial is cubic Let vi denote a corresponding unit-length is orthogonal, A eigenvector, and complete it to an orthonormal basis (vi, V2,Va) of R. Shou that the matriz representing f with respect to this basis has the...
(1 point) Compute the flux of the vector field F(x, y, z) = 3 + 2+ 2k through the rectangular region with corners at (1,1,0), (0,1,0), (0,0,2), and (1,0, 2) oriented in the positive Z-direction, as shown in the figure. 2.0 1.5 Flux = 0.0 12.0 11.5 2 1.0 0.5 0.0 2.94. god. og 9.500.00 [Enable Java to make this image interactive] (Drag to rotate) (1 point) Compute the flux of the vector field F(t, y, z) = 31 +23...
This Question: 2 pts 29 of 35 Given a two-dimensional vector field F and a smooth oriented curve C, what is the meaning of the flux of F across C? Choose the correct answer below A. The flux of F across C is the sum of the components of F tangent to C at each point of C. B. The flux of F across C is the component of F tangent to C at a point P on C O...
5. Setup (but do not evaluate) one integral (of any type) to find the flux of vector field F through surface S, where S s the unit cube given by 0 < x < 1,0 < y 1.0 < z 1,
5. Setup (but do not evaluate) one integral (of any type) to find the flux of vector field F through surface S, where S s the unit cube given by 0
a) A vector field F is called incompressible if div F = 0. Show
that a vector field of the form F = <f(y,z),g(x,z),h(x,y)> is
incompressible.
b) Suppose that S is a closed surface (a boundary of a solid in
three dimensional space) and that F is an incompressible vector
field. Show that the flux of F through S is 0.
c)Show that if f and g are defined on R3 and C is a closed curve
in R3 then...
A point-like charge of 5µC is located at the origin. Find the
flux of electric field
passing through a window at
defined by
and
.
Please use spherical cordinates and explain how you go about
solving this problem. Thank you
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