Find the circulation and flux for the field F(x, y) = (y – 6x² , x+y²) around and across the triangle given by y = 0, y = x, and x = 1.

Q: Find the flux of the vector field V(x, y, z) = 3xy²i + 5x²yj + 2z³k out of the unit sphere. Flux =

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Q: Express the vector field W = (x2 - y)a, + xza, in the (a) Cylinderical coordinate at P(p = 6, q =…

A: Cylindrical coordinates are ρ,ϕ,z now let us look at the general form of vector fieldW in…

Q: 1. Consider the vector field F(r, y) = -y²i+(x+2)j. (a) Evaluate F(0, 1). F(0,1) = (b) Sketch the…

A: Given:

Q: Find the gradient fields ƒ(x, y, z) = (x raise to the power 2 + y raise to the power 2 + z raise to…

A: Given:            f(x,y,z)=(x2+y2+z2)−12

Q: A uniform magnetic field B has constant strength b teslas in the z-direction [1.e., B = (0, 0, b) 1…

A: Stoke's theorem ∫CF→.dr→=∫∫S curlF→.dS→ Where S is a smooth surface bounded by a smooth closed curve…

Q: Find the curl, the divergence and the potential (if it exists) of F = (2x + y², 2ry + 3y²z*, 4y°z³)

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Q: (b) The square with vertices (0,0), (1, 0), (1, 1) and (0, 1), and the vector field F = 3x²yi + x³j.

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Q: A sodium ion (Na+) moves in the xy-plane with a speed of 2.90 ✕ 103 m/s. If a constant magnetic…

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Q: The magnetic field along a solenoid is conservative and given by 2xy 7- (2 x ₁-2x, (x²+1)-2). ¡−2x,…

A: Given a vector field as F=2xyx2+1-2x,lnx2+1-2 We need to find the scalar potential from which this…

Q: Find the flow of the field F = V(x²ze) once around the ellipse C in which the plane x + y + z = 1…

A: Consider the given field, F=∇x2zey around the ellipse in which the plane x+y+z=1intersects the…

Q: y² cos(xy?) – ay sin(æ²y) Let it be 7 : R² → R², (2ary cos (ay?) – ža² sin(a²y)/ a vector field.…

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Q: Suppose F(x, y) = (x² + 6y, 2x − 2y²). Use Green's Theorem to calculate the circulation of around…

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Q: Let F=(9xy,7y,8z)=(9xy,7y,8z). The curl of F=( Is there a function f such that F=∇f=∇?  (y/n)

A: The given function .We have to find the .

Q: An Eulerian flow field is described in Cartesian coordinates by V = 4i+xzj+5y3tk. (a) Is it…

A: According to bartlrby guidelines we have to answer only first three subparts please upload the…

Q: Sketch the slope field for the points (ti, y;) where at and dy dt y-2 Z₁ = -1 + 0.25(1-1) = for…

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Q: Use Green's Theorem to find the counterclockwise circulation and outward flux for the field F = (y -…

A: By using green theorem, we calculate the counterclockwise circulation and outward flux of the given…

Q: Sketch a directional field for the equation. Identify at least 3 isoclines. dy dx =y-x+2

A: This is a problem of slope field.

Q: For the vector field G = (yety + 4 cos(4x + y))i + (xey + cos(4x + y)) 5 I find the line integral of…

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Q: (a) Calculate the flux of the vector field F(x, y, z) = 3i – 9k through a sphere of radius 2…

A: We will use divergence theorem to find flux through the sphere of radius 2 centered at origin .

Q: F(1, y.:)= (x², 2x²y*, 5yz*) Given: Find (a) div F (b) curl F

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Q: Find the flow of the velocity field F = (y-x) - (x² + y²) j along each of the following paths from…

A: A velocity field is a vector field that describes the velocity of a fluid or a gas at each point in…

Q: For vector field F = (-2y, y), y > 0. Find all points P such that the amount of fluid flowing into P…

A: The vector field given is as follows: Fx, y=-2y, y We are asked to find points P=x, y such that the…

Q: Suppose that we want to estimate the parameter θ of the geometric distribution on the basis of a…

A: Introduction: Bayes' theorem is a fundamental concept of probability theory that describes the…

Q: Let F be the vector field (-2 sin(2x - y), sin(2x - y)). Find two non-closed curves C₁ and C₂ such…

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Q: You are given the velocity field:  v = y2i - x2j + z2k  Evaluate the divergence and curl of this…

A: Sol:- The velocity field is given by: v = y2i - x2j + z2k The divergence of the velocity field is…

Q: Let A be the vector potential and B the magnetic field of the infinite solenoid of radius R. Then 0…

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Q: Find the flux of F = z²k upward through the part of the sphere æ² + y² + z² = a² in the first octant…

A: Given vector field is  F=z2k to find the flux through sphere x2+y2+z2=a2 in the first octant.

Q: Find curl(F x G) = V x (F x G). F(x, y, z) = i + 9xj + 7yk G(x, y, z) = xi - yj + zk

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Q: ) Given vector field F (x, y) = 2y i + 3x j .Find the circulation of the vector field F over the…

A: The given problem is to find the circulation of vector field F over given circle of radius 2 ,…

Q: Evaluate the circulation of G = ayi+zj+ 7yk around a square of side 9, centered at the origin, lying…

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Q: Compute the curl of F = (3y2, ay, 22).

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Q: Let be a potential for the vector field F = (-24 x³z + 6 xyz², 3 x² z² + 15y¹, −6 x¹ + 6 x²yz - 10…

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