3. Calculate the rotational flow of F(x, y, z) = -j + xj + x²k, that goes through the cone given by x2 + y2 - z2 = 0 e 0
Q: 4. Let D = y²z°ãx + 2xyz³ ày + 3xy?z² đz pC/m² in free space. a. Find the total electric flux…
A: Solution:-
Q: Let F(x, y, z) = z tan-(y²)i + z³ In(x² + 2)j + zk. Find the flux of F across S, the part of the…
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Q: (1) Let F(x, y, 2) = (y², e* , 2). (a) Compute the divergence of F. (b) Use the divergence theorem…
A: As per our company guidelines, we are supposed to answer only first three sub-parts. Kindly repost…
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Q: Use divergence theorem to find the flux of F(x, y, z)=x²yî - xy²)+(2+2); o is the surface of the…
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Q: Use Divergence Theorem to evaluate SF. Nds and find the outward flux of F(x,y,z) = xi+y²j−zk through…
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Q: 2. The task is to determine the flux of B across G, where G is the positively-oriented portion of…
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Q: Find the flux of F = yi + 2zxj – z²k through the parabolic cylinder y = x2,0 < x < 1,0 < z< 4, in…
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Q: Let F(x, y, z) = z tan-1(y?)i + z In(x2 + 8)j + zk. Find the flux of F across S, the part of the…
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Q: b) Find the flux of the vector field F(x,y,z) = 3xi – yj + 2zk; across o where o is the portion of…
A: The given question belonging to the vector calculus in which we have to find the value flux of the…
Q: (c) Determine the flux of the vector field F = x³î – 2yĵ + 7z²k across a cone z = Jx2 + y2 + 3 that…
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Q: Evaluate the outward flux of the vector field F = (2x² – 5e" + sin(z²), –4ry + In(x*), 5z – 3x²y®)…
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Q: Find the flux of the field F(x, y, z) = 4x i + 4y j + 2 k outward (away from the z-axis) through the…
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Q: Let F(x, y, z) = z tan-¹(y²)i + z³ In(x² + 3)j + zk. Find the flux of F across S, the part of the…
A: The given problem is to find the flux of vector field over the given surface of part of the…
Q: (c) Determine the flux of the vector field F = x³î – 2yĵ + 7z²k across a cone z = J 8 by using…
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Q: Evaluate the outward flux of the vector field F = (2x? – 5e" + sin(2²), –4ry + ln(x*), 5z – 3x²y°)…
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Q: Suppose that v = (0, y, 0) is the velocity field of a fluid and let S be the surface defined by y =…
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Q: Let F(x, y, z) = z tan−1(y2)i + z3 ln(x2 + 10)j + zk. Find the flux of F across S, the part of…
A: let, F(x,y,z)=ztan−1(y2)i+z3ln(x2+10)j+zk Find the flux of F across the part of the…
Q: Let F(x, y, z) = z tan¬1(y²)i + z³ In(x² + 9)j + zk. Find the flux of F across S, the part of the…
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Q: Find the total flux of the field x+ /1+ y² + z² 2y + V1+x²+ z² \3z + /1+x² + y², F(x,y, z) = out of…
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Q: 17. Use the Divergence Theorem to find the outward flux across the boundary of the region D where F…
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Q: Find the work done by the force field F(x, y) = xi + 2yj on a particle moving along the path C:x =…
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Q: Given the radial field (x, y, z) (x² + y² + z²)³/2 |r|3/2 Find the outward flux across the sphere of…
A: Image is attached with detailed solution.
Q: Find the outward flux of the field F = 3xz2 i + y j - z3 k across the surface of the solid in the…
A:
Q: 2. Find the surface integral SS. ř · dS for the vector field F = xyî + yzĵ + zxk where S is part of…
A: To find Surface integral ∬SF→·dS→: The Surface S is of the form z=g(x,y) and is oriented upwards.…
Q: Let F(x, y, z) = z tan−1(y2) i + z3 ln(x2 + 8) j + z k. Find the flux of F across S, the part of the…
A:
Q: 7. Find the flux of F(z,y, 2) = ri+yj+zk through the portion of the paraboloid z = 1+z²+y° that is…
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Q: Let - (xz, 5 - 4xyz, xz) be the velocity field of a fluid. Compute the flux of i across the surface…
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Q: For the force field F = (2xe¬Y, (2y – x²e¬y)) in some open connected region containing P(1, 0) and…
A: Given that, F=2xe-y, 2y-x2e-y If F is conservative then ∂2F∂x∂y-∂2F∂y∂x=0
Q: 4. Calculate the flux of F = over the square shown below, oriented counterclockwise. SS (Px +Q, R…
A: We have to check given work on this problem write or wrong But this work is wrong Because flux or…
Q: 5. Use the Divergence theorem to calculate the z = 4 - x- flux of F across S where -x² + y? = 9 F =…
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Q: 6) Given a hemisphere bounded by S,: z = /25 – x2 – y? and S2:z = 0.Find the outward flux of the…
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A: Take dot product along limit of integration and integrate
Q: Use the Divergence Theorem to find the flux of F = xy2i + x2yj + yk outward through the surface of…
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Q: Let the surface Σ be the solid bounded by the paraboloid z “ 1 ´ x2 ´ y2 and the xy´plane.…
A: Use Gauss divergence theorem to compute the outward flux.
Q: Consider the force field F(x, y, z) = xi + yj + zk. Compute the work done in moving a particle along…
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Q: 2. Use the Divergence Theorem to calculate the flux of F(x, y, z) = (x³ + y) i+(y³ + 2³) j+(z³ + x²)…
A: The given vector field is F(x, y, z) = (x³ + y) i+ (y³ + z³) j+(x³ + x²) k across the surface of…
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A: Consider the given force field Fx,y=xyi+x2j Then, F⇀x,y=xy,y Write in parametric form y=t then…
Q: Let F(x, y, z) = z tan-1(y2)i + z3 In(x2 + 6)j + zk. Find the flux of F across S, the part of the…
A: Given that Fx,y,z=z tan-1y2i+z3Inx2+6j+2k Also, the part of paraboloid x2+y2+z=6 that lies above…
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- Show that 2xyz (x² + y²)² W = = (x² - y²)z (x² + y²)² y are the velocity (x² + y²) components of a possible liquid motion. Is this motion irrotational ?Double integrate under the hyperbolic paraboloid z=x2-y2 on the triangular footprint made by the x and y axes and the line y=-x+1? Thank youThe velocity field for a flow is given by V = ut + vj + wk where u = 3x, y = -2y and w = 2z. Find the streamline that will pass through the point (1, 1, 0).