Compute the flux of vector field V = .2 x +y2 x +y2 across the surface of the ellipsoid x2 y?, z2 + 1 a? b2 c2 oriented by the exterior normal. Select one: а. 4πο b. C. 3πC d. 2 πC e. Non of them

Q: What would you call the vector field V = yī – xj Solenoidal Solid Cylindrical Symmetric Irrotational

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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: Use the Divergence Theorem to calculate the flux of the vector fields F, = -2zi + 2xk and F2 = -2zi…

A: DIVERGENCE THEOREM I=∫∫∫div V dV=∫∫∫ ∇.V dV=∫∫V∫∂∂x+∂∂y+∂∂zdV GEOMETRICAL INTERPRETATION OF…

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: Find a flux of the vector field ä(M)= (2z– y)i +6xj + yk through a part of the surface S: x - 4y+2z…

A: Given, a→M=2z-yi^ +6x j^ +y k^ Also given surface is, S: x-4y+2z-4=0 So the normal vector to the…

Q: Find the flux of the vector field F(x, y, z) = ri across the outward oriented sphere %3D

A: In this question, we find the flux of the vector field f(x,y,z)=xi The surface is a sphere of radius…

Q: Find the flux of the vector field F k through the upper half of the sphere x + y + z² = 4. %3D pi…

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Q: Compute the flux of vector field V = x² +y? across the surface of the ellipsoid y? z? x² + y²" =D1…

A: Divergence theorem establishes the relationship between line integral and triple integral.…

Q: (a) Calculate the work done in moving a particle in the vector field: F = xz i+ xy?j + 3xzk along…

A: Given that : F = xz i + xy² j + 3xz k along the intersection of the plane x + z = M and the cylinder…

Q: Find the flux of the vector field F(x,y,z) = xi + yj+ 2zk across o, where o is the portion of the…

A: Flux of  a vector field F on the surface S   =∫∫SF ds We will use divergence theorem  If surface S…

Q: Find the flux of the vector field V(x, y, z) = 6xy²i + 7x<yj + z°k out of the unit sphere.

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Q: Consider the vector field F = = (x + y)i+ (x² + y² )j. What is the downward flux across the line…

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Q: Consider again the vector field F = (x +y)i + (x² + y²)j_what is the downward flux across the line…

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Q: Find the flux of the vector field F = 2r2i+ 2y²j+ 4k across o in the direction of positive…

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Q: Determine whether the vector field is conservative, and, if it is, find the potential function. (If…

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Q: calculate the flux of the vector field through the given surface. ~F = ~i + 2x~j + 4y ~k, and S is…

A: GIVEN: F = i + 2xj + 4yk Surface, z = 2x2 + y + 3

Q: Use Stoke's Theorem to determine the circulation of the vector field F (x, y, z) =(3y²) î – (cos z)j…

A: Solution:  Application of Stokes Theorem.

Q: Consider the following velocity vector field v = (2xz + y?) i + (2xy) j + (3z2 +x²) k, (a) Show that…

A: Hi! Thank you for the question, As per the honor code, we are allowed to answer one question at a…

Q: Q2) Find the flux of the vector field F(x,y,z) = (x,y, z) , where the surface S is the portion of…

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Q: Find the flux of the vector field F(x, y, z) 4y = "i+ 9 19 + Vr2 + y²k across S, where S is the…

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Q: Calculate the flux of the vector field (x°, y), out of the annular region between the a + y? = 16…

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Q: Calculate the flux of the vector field (x, y³), out of the annular region between the x? + y? = 1…

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Q: b) Given the vector field F(x,y,z) = 3z cosx i + xlny j + ez tanx k. Determine i. div F, ii. Vx F,…

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Q: Find the flux of the vector field F across the surface S in the indicated direction. F =x3y 2i+yj…

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Q: Compute the flux of the vector field F = across sphere a? + y² + z² = 9.

A: Let F be a vector field and S be the boundary of the surface D. To find the flux of the vector…

Q: Find the flux of the vector field F = through the half-sphere z = V1 - x² - y2. none of these above…

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Q: Integrate the vector field h(x,y) = y^2i + (2xy-e^2y)j over the circular arc C parametrized by r(t)…

A: The answer is given by using the formula of line integral

Q: (2, Y, z) : ze ye²) i + (2cos y ze²) j+ (e² rye²) k

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Q: Given the vector field F (x, y, z) = 2xyi + (x² + z?) j +2yzk a. Verify that the vector field…

A: Ans :A)

Q: The outward flux of the vector field F(x, y, z) = (x, y, z?) across the boundary of D = {(x, y, z) E…

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Q: Is the vector field F = [yze"yz, xze#yz, xye"yz] conservative? %3D O Yes O No

A: The vector field is conservative if ∇×F→=0 therefore, find ∇×F→ ∇×F→=ijk∂∂x∂∂y∂∂zyzexyzxzexyzxyexyz

Q: Find the flux of the vector field F across the surface S in the indicated direction. F = 8x i + 8y…

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Q: Compute the flux of the vector field F = zi + 8xk through the parameterized surface S oriented…

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Q: Find the flux of the vector field F across the surface S in the indicated direction. F = xi +yj+ z 2…

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Q: The vector field F = ( z, z²) has a scalar potential in the region R = {(x, y, z) E R° : x² + y? >…

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Q: (b) Verify Stokes Theorem for the vector field F = zî + xĵ + xk and the hemi- spherical shell S…

A: (b)  According to stokes theorem we have,

Q: Find the path integral of a particle moving along a straightline connecting O(0,0,0) to A(1,1,1)…

A: The path integral ∫OAF·dr involves the integration over a specific path, where F is a vector-valued…

Q: What is the value of a so that the vector field F(x.y)=(y eX+2xy4) i+(ax2y3+ e%) j is conservative?…

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Q: Determine whether the vector field is conservative, and, if so, find a potential function. (If the…

A: If curl of vector field is zero then conservative otherwise not conservative

Q: 2u?u? Σ: y = u with 0<u < 2,0 < v< 1. Z = V

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Q: Calculate the flux of the vector field (a, y°), out of the annular region between the a2 + y? = 1…

A: According to the flux form of Greens Theorem for a region containing hole, the flus ix defined by…

Q: Find the flux of the vector field F(x, y, z) = 3i– 7 j+ zk where o is the portion of the cylinder x…

A: We need to find the flux of the given vector field F(x, y, z) = 3i - 7j + zk where σ is the portion…

Q: Find the flux of the force field F(x, y, 2) = (2, x + r², 1 – a² + y) across the portion of the…

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Q: Determine whether the vector field is conservative, and, if it is, find the potential function. (If…

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Q: Consider the vector field F (x+ y)i + (x² + y²)j What is the downward flux across the line segment…

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Q: Find the outward flux of the given field across the given cardioid. F=(3ry-)i+(e*+5tan-'y)j 1+y?…

A: The outward flux of given field is given by using greens theorem.

Q: Find the flux of the vector field J = 2x?yi + 4zj ou t of the closed box 0 < x < 2,0 < y< 8,0 < z <…

A: We have to find the flux

Q: Determine the flux of the vector field F = x³i – 2yĵ + 7z?k across a cone z = /x2 + y2 + 3 that lies…

A: Gauss theorem states that if V is a volume inclosed by a closed surface S then  flux=∫∫S F.n dS=∬∫V…

Q: Calculate the flux of the vector field through the given surface. F = zi + 2xj + 3yk, and S is the…

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Q: Sketch the vector field F(x, y) = 3i + 5j and calculate the flux then the circulation of F| along…

A: (1) The equation of line segment is: x+3-2+3=y-1-5-1=tx+3=t⇒x=t-3y-1=-6t⇒y=-6t+1 The curve…