(8pts)Consider the following vector field F and closed oriented curve C in the plane a. compute...

(8pts)Consider the following vector field F and closed oriented curve C in the plane

a. compute the circulation and interpret the result

b. compute the flux of the vector field F across C

F = <y,-2x>/sqrt(4x^2+y^2)

r(t) = <2cost,4sint>

Solutions

Expert Solution

milcah answered 1 year ago

Next > < Previous

Related Solutions

Compute the flux of the vector field F = <xy, 5yz, 6zx> through the portion of...

Compute the flux of the vector field F = <xy, 5yz, 6zx> through the portion of the plane 3x + 2y + z = 6 in the first octant with the downward orientation.

Determine which of the following vector fields F in the plane is the gradient of a...

Determine which of the following vector fields F in the plane is the gradient of a scalar function f. If such an f exists, find it. (If an answer does not exist, enter DNE.) F(x, y) = 3xi + 3yj f(x, y) = F(x, y) = 6xyi + 6xyj f(x, y) = F(x, y) = (4x2 + 4y2)i + 8xyj f(x, y) =

Use the extended divergence theorem to compute the total flux of the vector field F(x, y,...

Use the extended divergence theorem to compute the total flux of the vector field F(x, y, z) = −3x2 + 3xz − y, 2y3 − 6y, 9x2 + 4z2 − 3x outward from the region F that lies inside the sphere x2 + y2 + z2 = 25 and outside the solid cylinder x2 + y2 = 4 with top at z = 1 and bottom at z = −1.

Using Green’s theorem, compute the line integral of the vector field below, along the curve x^2...

Using Green’s theorem, compute the line integral of the vector field below, along the curve x^2 - 2x + y^2 = 0 , with the counterclockwise orientation. Don’t compute the FINAL TRIG integral. F(x,y) = < (-y^3 / 3) - cos(x^7) , cos(y^9 + y^5) + (x^3 / 3) > .

Compute the line integral of the vector field F(x, y, z) = ⟨−y, x, z⟩ along...

Compute the line integral of the vector field F(x, y, z) = ⟨−y, x, z⟩ along the curve which is given by the intersection of the cylinder x 2 + y 2 = 4 and the plane x + y + z = 2 starting from the point (2, 0, 0) and ending at the point (0, 2, 0) with the counterclockwise orientation.

Using Green’s theorem, compute the line integral of the vector field below, along the curve x^2-2x+...

Using Green’s theorem, compute the line integral of the vector field below, along the curve x^2-2x+ y^2=0 , with the counterclockwise orientation. Don’t compute the FINAL TRIG integral. F(x,y)=<- y^3/3-cos⁡(x^7 ) ,cos(y^9+y^5 )+ x^3/3> .

1.For an angle of zero between the magnetic field and the vector normal to the plane...

1.For an angle of zero between the magnetic field and the vector normal to the plane of the coil: (a) What happens to the light bulb as it enters the magnetic field region? Explain. (b) What happens to the light bulb as it moves while it is completely inside the magnetic field? Explain. (c) What happens to the light bulb as it exits the magnetic field region? NOTE: Use Faraday’s Law to explain. 2.For an angle of zero between the...

Evaluate the surface integral S F · dS for the given vector field F and the...

Evaluate the surface integral S F · dS for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the positive (outward) orientation. F(x, y, z) = xy i + yz j + zx k S is the part of the paraboloid z = 6 − x2 − y2 that lies above the square 0 ≤ x ≤ 1, 0 ≤ y ≤ 1, and has...

Evaluate the surface integral S F · dS for the given vector field F and...

Evaluate the surface integral S F · dS for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the positive (outward) orientation. F(x, y, z) = x i − z j + y k S is the part of the sphere x2 + y2 + z2 = 1 in the first octant, with orientation toward the origin

Evaluate the surface integral S F · dS for the given vector field F and...

Evaluate the surface integral S F · dS for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the positive (outward) orientation. F(x, y, z) = x i − z j + y k S is the part of the sphere x2 + y2 + z2 = 9 in the first octant, with orientation toward the origin

Subjects