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Problem 3. In each image below, we have a cross section of a 3D vector field...
(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...
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.
2. Determine whether there is a potential function for the vector field V= <yz, xz, xy>....
2. Determine whether there is a potential function for the vector field V= <yz, xz, xy>. You may use any legitimate method but you must justify your claim. If it there is a potential function, then find it and use it to evaluate the line integral ſ v.dr along the curve r(t) = <V7,4-4,6+1>ifor Osts 4. [10] 4. Suppose S is the surface z= x² + 4y’, lying beneath the plane z=1. Orient S by taking the inner normal n...
A uniform electric field is produced due to the charge distribution inside the closed cylindrical surface...
A uniform electric field is produced due to the charge distribution inside the closed cylindrical surface (a) What type of charge distribution is inside the surface? C a positive line charge situated on and parallel to the axis of the cylinder O a negatively charged plane parallel to the end faces of the cylinder C a positively charged plane parallel to the end faces of the cylinder a collection of negative point charges arranged in a line at the center...
(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...
The magnetic field in a region of space is given by: Ba(x2+22)7+(y2+22)7+(x2+z2)k) where alpha is some...
The magnetic field in a region of space is given by: Ba(x2+22)7+(y2+22)7+(x2+z2)k) where alpha is some constant, x, y, and z are the coordinates in space about the origin and i, j, and k are unit vectors pointing along the x, y, and z-axes Also in the region of space is a conducting square loop with side lengths of L which is placed parallel to the xy-plane, centered on the z-axis, and has a z-coordinate of z Find an expression...
2. Calculate the flux of the vector field F (2ry,-y2 + 3y, 1) through the surface with boundary S...
2. Calculate the flux of the vector field F (2ry,-y2 + 3y, 1) through the surface with boundary Soriented with the outward unit normal in the figure below. Assume the volume of the solid E which lies inside the surface S and above the ry plane is 2π. Follow the following steps. [Warning: The problem is very similar to the one in PS11 but they are not the same. We can not apply the Divergence Theorem to S since it...
ELECTRIC FIELD AND FLUx EM HW-81 Name 3. The loop shown at right has an area...
ELECTRIC FIELD AND FLUx EM HW-81 Name 3. The loop shown at right has an area A. The loop is held to the right of a positive point charge as shown Loop of area A a. i. Draw and label an area vector for the surface bounded by the loop. Front of loop Back of loop ii. Sketch electric field lines to represent the electric field due to the charge. ? Explain Is the electric flux through the loop due...
We'll work througil uhe caitul 3. In this problem, of the electric field near the surface of a la...
we'll work througil uhe caitul 3. In this problem, of the electric field near the surface of a large, flat metal conductor. In the image at right, the square represents a section of the conductor's surface. The region above the surface is empty space, and below the surface is solid conducting metal. There is a uniform positive surface charge density +σ on the surface of the conductor. R I What is the electric field inside the conductor? Explain your reasoning....
(1 point) Horizontal cross-sections of the vector fields F(x, y, z) and G(x, y, z) are...
(1 point) Horizontal cross-sections of the vector fields F(x, y, z) and G(x, y, z) are given in the figure. Each vector field has zero z-component (i.e., all of its vectors are horizontal) and is independent of 2 (i.e., is the same in every horizontal plane). You may assume that the graphs of these vector fields use the same scale. (a) Are div(F) and div(G) positive, negative, or zero at the origin? Be sure you can explain your answer. At...
(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...
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.
2. Determine whether there is a potential function for the vector field V= <yz, xz, xy>. You may use any legitimate method but you must justify your claim. If it there is a potential function, then find it and use it to evaluate the line integral ſ v.dr along the curve r(t) = <V7,4-4,6+1>ifor Osts 4. [10] 4. Suppose S is the surface z= x² + 4y’, lying beneath the plane z=1. Orient S by taking the inner normal n...
A uniform electric field is produced due to the charge distribution inside the closed cylindrical surface (a) What type of charge distribution is inside the surface? C a positive line charge situated on and parallel to the axis of the cylinder O a negatively charged plane parallel to the end faces of the cylinder C a positively charged plane parallel to the end faces of the cylinder a collection of negative point charges arranged in a line at the center...
(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...
The magnetic field in a region of space is given by: Ba(x2+22)7+(y2+22)7+(x2+z2)k) where alpha is some constant, x, y, and z are the coordinates in space about the origin and i, j, and k are unit vectors pointing along the x, y, and z-axes Also in the region of space is a conducting square loop with side lengths of L which is placed parallel to the xy-plane, centered on the z-axis, and has a z-coordinate of z Find an expression...
2. Calculate the flux of the vector field F (2ry,-y2 + 3y, 1) through the surface with boundary Soriented with the outward unit normal in the figure below. Assume the volume of the solid E which lies inside the surface S and above the ry plane is 2π. Follow the following steps. [Warning: The problem is very similar to the one in PS11 but they are not the same. We can not apply the Divergence Theorem to S since it...
ELECTRIC FIELD AND FLUx EM HW-81 Name 3. The loop shown at right has an area A. The loop is held to the right of a positive point charge as shown Loop of area A a. i. Draw and label an area vector for the surface bounded by the loop. Front of loop Back of loop ii. Sketch electric field lines to represent the electric field due to the charge. ? Explain Is the electric flux through the loop due...
we'll work througil uhe caitul 3. In this problem, of the electric field near the surface of a large, flat metal conductor. In the image at right, the square represents a section of the conductor's surface. The region above the surface is empty space, and below the surface is solid conducting metal. There is a uniform positive surface charge density +σ on the surface of the conductor. R I What is the electric field inside the conductor? Explain your reasoning....
(1 point) Horizontal cross-sections of the vector fields F(x, y, z) and G(x, y, z) are given in the figure. Each vector field has zero z-component (i.e., all of its vectors are horizontal) and is independent of 2 (i.e., is the same in every horizontal plane). You may assume that the graphs of these vector fields use the same scale. (a) Are div(F) and div(G) positive, negative, or zero at the origin? Be sure you can explain your answer. At...
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