Compute the flux of the vector field  F=2xi+2yj through the surface S, which is the part of the surface z=36−(x^2+y^2) above the disk of radius 6 centered at the origin, oriented upward. flux = _____

Q: Find the curl of the vector field F =

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Q: Find the flux through the top, left, and right sides of a cube of side 0.5 m when placed in a…

A: Side of a cube,(l)=0.5 m ------(1) [Given] Horizontal uniform electric field,(E)=8 N/C ------(2)…

Q: Given a scalar field V(x, y) = x² + y°, a unit normal vector to V is O a. (2y) +- 4x2+4y? O b. (2x)…

A: Give that scalar field V(x,y)=x^2+y^2.

Q: Charges q1 and q2 are placed on the y-axis at y = 0 and y = 27.7 m, respectively. If q1 = −40.1 pC…

A: It is given that,

Q: Use the Divergence Theorem to find the outward flux of F = =(%x* + 12xy²) i+ (5y³ + 5e'sin z) j+…

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Q: ges lle in plane, Four Gaussian surfaces ch enclose part of this plane and the image shows the…

A: According to Gauss's theorem Electric flux = qenc /ε₀

Q: Find the k-component of (curl F) for the following vector field on the plane. F = (xe)i + (8y ex)j…

A: The vector field on the plane is given as F=xeyi^+8yexj^

Q: Find the flux through the top, left, and right sides of a cube of side 1.75 m when placed in a…

A: The electric flux via the cube’s sides can be represented as, Here, E and A represent the electric…

Q: Find the flux of the vector field F = (y, – z, x) across the part of the plane z = 1+ 3x + 2y above…

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Q: z4 k across the surface S the upper hemisphere of x 2 + y 2 +z2 = 9 in the outward direction Find…

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Q: Find the net electric flux through each of the following closed surfaces: 1. G1 2. R2 3. Аз 4. Сд 5.…

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Q: Consider the vector field F = zi + a2j+ (y3 + 3z)k Calculate the divergence: V.F = Calculate the…

A: "Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Consider the field F (x, y, z) = 2yj^-> and the sphere centered at the origin of radius a. We can…

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Q: Verify if the following vector fields are conservative: a) A₁ (+-) 1 = b) ₂ = (xy, yz, zx) c) A3 =…

A: We have given three vector fields , we need to see whether they are conservative or not. If…

Q: Calculate the electric flux through the gaussian surface represented by the dashed line, in N m2 / C

A: Given  Q1 = -30.2 x 10^{-12} C, Q2 = -9 x 10^{-12 }C, Q3 = 27 x 10^{-12} C, Q4 = 3.9 x 10^{-12} C,…

Q: Two hemispherical surfaces, 1 and 2, of respective radii r1 and r2, are centered at a point charge…

A: The flux can be calculated as follows,

Q: The divergence of a vector field F(x,y, z) = xy'i+ 2r?yzj - 3yz²k at the point (1,-1,1) is 9. -3 3.…

A: F(x,y,z) = xy2i^ + 2x2yzj^ - 3yz2k^Point (P) = (1,-1,1)

Q: Find the flux through the top, left, and right sides of a cube of volume 27 m3 when placed in a…

A: Given, The volume of cube = 27 m3 Electric field = 2.25 N/C

Q: Find the upward flux of the vector field F(x.y,z)= (-y, x, 9) across the part of the hemisphere…

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Q: Compute for the magnitude of the line integral over a square path centered on p(0,0) with a side…

A: Line integral over a squared path centered on p(0.0) for a field B→ is given by…

Q: The net flux of the vector field A 3pp through the closed surface defined by p= 3,0 < z< 5,0 < p<…

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Q: Find the net outward flux of the field F = (7y- z,z,7y - 5x) across the sphere of radius 6 centered…

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Q: Consider the field F(x,y,z)=2y j and the sphere centered at the origin of radius a. We can conclude…

A: This problem can be easily solved by using the law of Gauss's divergence theorem. Which state that…

Q: The vector field D* = e*r (cos2q) r3 is defined within the spherical shell whose inner and outer…

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Q: Compute the flux of the vector field F = through the surface S where S is the surface bounded by r=…

A: Write the given values of this problem. F→=&lt;r2+sin2θ,rsinθ cosθ,3z&gt;Bounded surface=Sr=2, Z=0,…

Q: Two conductors with concentric radii r1%39 m and r2%3D15 m are placed in such a way that their…

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Q: Suppose a twodimensional force field is everywhere directed outward from the origin, and C is a…

A: It is given that the two-dimensional force field is directed outward from the origin everywhere.…

Q: Compute the flux of the vector field F = 2zk through S, the upper hemisphere of radius 6 centered at…

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Q: Charges q1 and q2 are placed on the y-axis at y = 0 and y = 27.9 m, respectively. If q1 = −41.2 pC…

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Q: Find the net flux o passing through the following Gaussian surface S. -4µc - 6µC 4μC 5με 9µC

A: Introduction: According to Gauss's law, the total electric flux of a hypothetical Gauss's closed…

Q: Let F(r, y, 2) = 3z7- 2y 3 – (x + y) E. For each of the surfaces in Parts (a)-(d), say whether the…

A: Hi. Since you have posted a question with multiple subparts and not specified which subparts you…

Q: 3. Compute the electric flux of the following sets of variables: a. E = 7.2 x 105 N/C %3D A = 4.4 x…

A: Electric flux φ = E̅•A̅     = E A Cosθ

Q: Find the flux of the vector field F = k through the upper half of the sphere r? + y² + z2 = 4. 4pi…

A: Sphere : x2 + y2 +z2 =4 Radius = 40.5            = 2 units

Q: Let C be the unit circle oriented in the counterclockwise direction. Calculate the outward flux of…

A: Given- F(x,y)=&lt;x3+siny,y3+cosx2&gt;

Q: Find the flux through the top, left, and rights sides of a cube of side 0. 3 m when placed in a…

A: Given data: Length of side of cube is, a=0.3 m. Magnitude of electric field is, E=8.0 N/C…

Q: 1. Find the flux through a spherical Gaussian surface of radius a = 1 m surrounding a charge of 8.85…

A: according to gauss law if any cosed surface contains the net  charge  q inside its surface then the…

Q: Two conductors with concentric radii r1=13 m and r2-26 m are placed in sudch a way that their center…

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Q: Please answer and write correctly and neatly. A certain vector field is given as G = (y + 1)ax +…

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Q: A vector field is given by F = y'e*i - x*yj - xtan-'yk use the divergence (Gauss") theorem, to…

A: Given:-             F→ = y3ezi^ -x2y j^ -xtan-1y k^

Q: . If a vector field A(x,y,z)=xz'ex - 2x°yzey+2yz´ez , calculate the curl 7xA at point M(1,-1,-1).

A: In vector calculus, the curl of a vector field is a quantity that describes the infinitesimal…

Q: Compute the curl of the vector field F(r, 6,0) in spherical coordinates.

A: To find out: Curl of the vector field in spherical polar coordinate: F→(r,θ,ϕ)=re^θ+e^ϕ

Q: Compute the flux of the vector field F = 2zk through S, the upper hemisphere of radius 5 centered at…

A: The flux over a closed surface can be calculated via the divergence theorem using the formula

Q: Given a vector field D = 2xy² ax + x² av and the rectangular parallel pipe formed by the planes x =…

A: Given: The vector field , Here , x , y, z are the planes of a rectangular parallel pipe. The flux…

Q: For each of the following vector fields F , decide whether it is conservative or not by computing…

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Q: Four small spheres shown in the figure below have charges of q1 = -3.00 nC, q2 = 2.40 nC, q3 = 5.30…

A: Given problem is based on the Gauss’s law in electrostatics. It states that, “The net electric flux…

Electric Charges and Fields

One of the fundamental properties is the electromagnetic property. Charge cannot be destroyed by any process and this contributes formally to the law of charge conservation.