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Dr for F For which of the following situation is Green's/Stokes (r-1) +(-Iy applicable? Include y...
7. Use Green's Theorem to find Jc F.nds, where C is the boundary of the region bounded by y = 4-x2 and y = 0, oriented counter-clockwise and F(x,y) = (y,-3z). what about if F(r, y) (2,3)? x2...
7. Use Green's Theorem to find Jc F.nds, where C is the boundary of the region bounded by y = 4-x2 and y = 0, oriented counter-clockwise and F(x,y) = (y,-3z). what about if F(r, y) (2,3)? x2 + y2 that lies inside x2 + y2-1. Find the surface area of this 8. Consider the part of z surface. 9. Use Green's Theorem to find Find J F Tds, where F(x, y) (ry,e"), and C consists of the line segment...
In each of the following exercises, you are given a force field F = F(x, y),...
In each of the following exercises, you are given a force field F = F(x, y), in Newtons, and a oriented, closed curve C in the xy-plane, where x and y are in meters. Use Green's Theorem to calculate the work done by F along C. 9. F(x, y) = (2,5 – yº, x3 – y5), and C is the curve which starts at (0,0), moves along a line segment to (1/V2,1/V2), moves counterclockwise along the circle of radius 1,...
Prob. 12.8 Criticize the following 'proof that r = 0. (a) Apply Green's theorem in a...
Prob. 12.8 Criticize the following 'proof that r = 0. (a) Apply Green's theorem in a plane to the functions P(x, y) = tan-(y/x) and Q(x, y) = tan-'(x/y), taking the region R to be the unit circle centered on the origin. (b) The RHS of the equality so produced is S SR dxdy, which, either from symmetry considerations or by changing to plane polar coordinates, can be shown to have zero value. (c) In the LHS of the equality,...
3. Consider the vector field F(x, y) + 2y F dr, where C is the circle (r-2)2 +y2 = 1, oriented counterclock (a) Com...
3. Consider the vector field F(x, y) + 2y F dr, where C is the circle (r-2)2 +y2 = 1, oriented counterclock (a) Compute wise (Hint: use the FT of line integrals. We could not use it for the circle centered at the origin, but we can use the theorem for this circle. Why?) (b) Let 0 be the angle in polar coordinates for a point (x, y). Check that 0 is a potential function for F
3. Consider the...
1. Magnetic Field Generated by a Current in a Wire Under steady-state conditions, a magnetic fiel...
1. Magnetic Field Generated by a Current in a Wire Under steady-state conditions, a magnetic field B has curlB in a region where there is no current. We study the steady-state magnetic field B due to a constant current in an infinitely long straight thin wire. The magnitude of the magnetic field at a point depends only on the distance from the wire and its direction is tangent to the circle around the wire and determined by the right-hand rule....
1 Use Stokes' theorem to evaluate the integrals: F(x, y, z) dr a) where F(r, y,z)(3yz,e, 22) and C is the boundary of the triangle i the plane y2 with vertices b) where F(x, y,z (-2,2,5xz) an...
1 Use Stokes' theorem to evaluate the integrals: F(x, y, z) dr a) where F(r, y,z)(3yz,e, 22) and C is the boundary of the triangle i the plane y2 with vertices b) where F(x, y,z (-2,2,5xz) and C is in the plane 12- y and is the boundary of the region that lies above the square with vertices (3,5, 0), (3,7,0),(4,5,0), (4,7,0) c) where F(x, y,z(7ry, -z, 3ryz) and C is in the plane y d) where intersected with z...
(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...
G00 Rapid move G0 X# Y# Z# up to eight axes or GO Z# X# Gol Feed Rate move G 1 X# Y# Z# up to eight axes or G1 Z# X# G02 Clockwise move X# Y#1# J# G03 Counter Clockwise move X# Y#1# G04 Dwell time G0...
G00 Rapid move G0 X# Y# Z# up to eight axes or GO Z# X# Gol Feed Rate move G 1 X# Y# Z# up to eight axes or G1 Z# X# G02 Clockwise move X# Y#1# J# G03 Counter Clockwise move X# Y#1# G04 Dwell time G04 L# G08 Spline Smoothing On G09 Exact stop check, Spline Smoothing Off G10 A linear feedrate controlled move with a decelerated stop G11 Controlled Decel stop G17 XY PLANE G18 XZ PLANE...
7. Use Green's Theorem to find Jc F.nds, where C is the boundary of the region bounded by y = 4-x2 and y = 0, oriented counter-clockwise and F(x,y) = (y,-3z). what about if F(r, y) (2,3)? x2 + y2 that lies inside x2 + y2-1. Find the surface area of this 8. Consider the part of z surface. 9. Use Green's Theorem to find Find J F Tds, where F(x, y) (ry,e"), and C consists of the line segment...
In each of the following exercises, you are given a force field F = F(x, y), in Newtons, and a oriented, closed curve C in the xy-plane, where x and y are in meters. Use Green's Theorem to calculate the work done by F along C. 9. F(x, y) = (2,5 – yº, x3 – y5), and C is the curve which starts at (0,0), moves along a line segment to (1/V2,1/V2), moves counterclockwise along the circle of radius 1,...
Prob. 12.8 Criticize the following 'proof that r = 0. (a) Apply Green's theorem in a plane to the functions P(x, y) = tan-(y/x) and Q(x, y) = tan-'(x/y), taking the region R to be the unit circle centered on the origin. (b) The RHS of the equality so produced is S SR dxdy, which, either from symmetry considerations or by changing to plane polar coordinates, can be shown to have zero value. (c) In the LHS of the equality,...
3. Consider the vector field F(x, y) + 2y F dr, where C is the circle (r-2)2 +y2 = 1, oriented counterclock (a) Compute wise (Hint: use the FT of line integrals. We could not use it for the circle centered at the origin, but we can use the theorem for this circle. Why?) (b) Let 0 be the angle in polar coordinates for a point (x, y). Check that 0 is a potential function for F
3. Consider the...
1. Magnetic Field Generated by a Current in a Wire Under steady-state conditions, a magnetic field B has curlB in a region where there is no current. We study the steady-state magnetic field B due to a constant current in an infinitely long straight thin wire. The magnitude of the magnetic field at a point depends only on the distance from the wire and its direction is tangent to the circle around the wire and determined by the right-hand rule....
1 Use Stokes' theorem to evaluate the integrals: F(x, y, z) dr a) where F(r, y,z)(3yz,e, 22) and C is the boundary of the triangle i the plane y2 with vertices b) where F(x, y,z (-2,2,5xz) and C is in the plane 12- y and is the boundary of the region that lies above the square with vertices (3,5, 0), (3,7,0),(4,5,0), (4,7,0) c) where F(x, y,z(7ry, -z, 3ryz) and C is in the plane y d) where intersected with z...
(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...
G00 Rapid move G0 X# Y# Z# up to eight axes or GO Z# X# Gol Feed Rate move G 1 X# Y# Z# up to eight axes or G1 Z# X# G02 Clockwise move X# Y#1# J# G03 Counter Clockwise move X# Y#1# G04 Dwell time G04 L# G08 Spline Smoothing On G09 Exact stop check, Spline Smoothing Off G10 A linear feedrate controlled move with a decelerated stop G11 Controlled Decel stop G17 XY PLANE G18 XZ PLANE...
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