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2. Consider the vector field F = x21 + y2J shown below. For boih poinis I'...
2. Consider the vector field F = (z v)a I zy (z + a)2. Consider also...
2. Consider the vector field F = (z v)a I zy (z + a)2. Consider also a frustum of cone defined as: (see figure). Let us call V the volume of this solid. Alio, let S be the closed surface enclosing the volume: S -S1 U S2 U S3, where Si is the flat bottom (z = 1), S2 is the curved surface and Ss is the flat top (z 4). (a) calculate the flux Ф-ISF ds, using the appropriate...
(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...
(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...
5. Surface integral of a vector field (10%) Consider the vector field F = fkır +...
5. Surface integral of a vector field (10%) Consider the vector field F = fkır + ĉk2x. Evaluate the surface integral ſ F. ds over the surface of a closed cylinder about the z-axis specified by z = +3 and r = 2. (The cylinder has a height of 6 and a radius of 2.) The cylinder is illustrated below.
3) Consider the vector field F-ra where a is a constant vector and let V be the region in R3 bounded by the surfaces r y24,1, z0. Find the outward flux of F i1n across the closed surface S of V...
3) Consider the vector field F-ra where a is a constant vector and let V be the region in R3 bounded by the surfaces r y24,1, z0. Find the outward flux of F i1n across the closed surface S of V
3) Consider the vector field F-ra where a is a constant vector and let V be the region in R3 bounded by the surfaces r y24,1, z0. Find the outward flux of F i1n across the closed surface S...
8.) (12 pts.) Find the Flux of the Vector Field F(x, y, z) = (z)i +...
8.) (12 pts.) Find the Flux of the Vector Field F(x, y, z) = (z)i + (x)} + (y)k through Surface S, which is that portion of the plane 2++2 = 3 is the 1st octant, and r is the unit normal vector pointing away from the origin.
9. X-rays have intensity and direction that are given by a vector field F(x, y, z)...
9. X-rays have intensity and direction that are given by a vector field F(x, y, z) = (z?, sin(2) +y +278, z + cos(x) + sin(xy)). A tonsil (shown below) is given in spherical coordinates as p < 0. Find the flux of the X-ray field F through the surface p = 0 of the tonsil. The surface is oriented with outward pointing normal vectors.
(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
(1 point) Determine whether the flux of the vector field F through each surface is positive, nega...
(1 point) Determine whether the flux of the vector field F through each surface is positive, negative, or zero. In each case, the orientation of the surface is indicated by the gray normal vector. Enable Java to Enable Java to [Enable Java to make this image make this image make this image interactive] interactive] interactive Choose Choose Choose Enable Java to [Enable Java to make this image make this image interactive] interactive] Choose Choose
(1 point) Determine whether the flux...
question 5 b why tge elecric field lines are the same in both sides i dont...
question 5 b
why tge elecric field lines are the same in both sides i dont
understand why?
Spring 2019 Exam 2 2 5. A small portion near the center of a very thin sheet with surface charge density +0o is shown. A cylindrical Gaussian surface of radius a encloses part of the sheet. Let Et and ER represent the magnitude of the electric field at the left and right ends of the cylinder, which are different distances from the...
2. Consider the vector field F = (z v)a I zy (z + a)2. Consider also a frustum of cone defined as: (see figure). Let us call V the volume of this solid. Alio, let S be the closed surface enclosing the volume: S -S1 U S2 U S3, where Si is the flat bottom (z = 1), S2 is the curved surface and Ss is the flat top (z 4). (a) calculate the flux Ф-ISF ds, using the appropriate...
(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...
(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...
5. Surface integral of a vector field (10%) Consider the vector field F = fkır + ĉk2x. Evaluate the surface integral ſ F. ds over the surface of a closed cylinder about the z-axis specified by z = +3 and r = 2. (The cylinder has a height of 6 and a radius of 2.) The cylinder is illustrated below.
3) Consider the vector field F-ra where a is a constant vector and let V be the region in R3 bounded by the surfaces r y24,1, z0. Find the outward flux of F i1n across the closed surface S of V
3) Consider the vector field F-ra where a is a constant vector and let V be the region in R3 bounded by the surfaces r y24,1, z0. Find the outward flux of F i1n across the closed surface S...
8.) (12 pts.) Find the Flux of the Vector Field F(x, y, z) = (z)i + (x)} + (y)k through Surface S, which is that portion of the plane 2++2 = 3 is the 1st octant, and r is the unit normal vector pointing away from the origin.
9. X-rays have intensity and direction that are given by a vector field F(x, y, z) = (z?, sin(2) +y +278, z + cos(x) + sin(xy)). A tonsil (shown below) is given in spherical coordinates as p < 0. Find the flux of the X-ray field F through the surface p = 0 of the tonsil. The surface is oriented with outward pointing normal vectors.
(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
(1 point) Determine whether the flux of the vector field F through each surface is positive, negative, or zero. In each case, the orientation of the surface is indicated by the gray normal vector. Enable Java to Enable Java to [Enable Java to make this image make this image make this image interactive] interactive] interactive Choose Choose Choose Enable Java to [Enable Java to make this image make this image interactive] interactive] Choose Choose
(1 point) Determine whether the flux...
question 5 b
why tge elecric field lines are the same in both sides i dont
understand why?
Spring 2019 Exam 2 2 5. A small portion near the center of a very thin sheet with surface charge density +0o is shown. A cylindrical Gaussian surface of radius a encloses part of the sheet. Let Et and ER represent the magnitude of the electric field at the left and right ends of the cylinder, which are different distances from the...
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