Identify the work done, J. F.dr by an electric field, E = (x + xy)î + (y + 5)f – 5zk V/m to move an electron along path C, where it is a portion of = 1 that is in the fourth quadrant with counter clockwise direction and stop at position (0, 0, 2) as shown

Q: Find the work done by the force F = 9xy i + 6yj acting along the piecewise-smooth curve consisting…

A: Given that F=9xy i+6y2 j Let r=xi+yj+zk ⇒dr=dx i+dy j+dz k Now,  F.dr=(9xy i+6y2 j+0k)(dx i+dy j+dz…

Q: 1. Calculate the line integral f F-d7, where F (z. y, 2) = -y? +z3 +zk and C is the path C along the…

A: This is a problem from line integral.

Q: If the electric potential at a point (x, y) in the xy-plane is V(x, y), then the electric intensity…

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Q: Give a parametric representation for the path followed by a heat seeking particle placed at point P…

A: The given temperature field is T(x,y)=64-x2-y3------(1) P(4,2) is the given point Then the gradient…

Q: Evaluate the line integral F· dr where F (3 sin z, -5 cos y, 5cz) and C is the path given by r(t) =…

A: Line integral is integral of some function along a curve or path. Any field for which the line…

Q: Evaluate the line integral C: y² = 27x from (27, 27) to (0,0). NOTE: Enter the exact answer. 6-₂…

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Q: 6: Find the work done by the force F = -7y i+ 10x j along one loop of the curver = sin 70 (in the…

A: Given

Q: Evaluate the line integral [21r²yzds with respect to s along the 2 curve C : x = t₁ y = t², z =…

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Q: Find the work done by the force field F in moving a particle along the curve C. F(x, y) = (x - y°)i+…

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Q: (a) Evaluate feay'ds with C being the right half of the circle + y - 16. Does it depend on…

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Q: The work done by the force F = in the displacement along the path C:y=x² from the point (0,0) to…

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Q: (b) Find the derivative of g in the direction of a=2i+curl w at point (0,-1,1) where u u +2 g= In. J…

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Q: 4. Find the work done by the force field F = (x? sin(y),y) on a particle that moves along the cubic…

A: Given: The force field, F→=x2siny,y on a particle that moves along the cubic y=x3 from 1,1 to 2,8.

Q: Use a scalar line integral to find the length of the curve r(t) = (20 sin , 20 cos ,5), for 0 < t <…

A: Given

Q: (1) (a) Show that the line integral tan(y) dr +x sec (y) dy is independent of path, where C is any…

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Q: Evaluate the line integral F. dr where F = (3 sin x, 3 cos y, 10xz) and C is the path given by r(t)…

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Q: Find the work done under the influence of the force E = 3xyi – 5zj + 10xk along the curve x= t² + 1,…

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Q: Consider the curve r(t) = (t, 3 cos t, 3 sin t) for t > 0. COS So r(t)dt Compute the integral above.

A: ∫0πr(t)dt=∫0π&lt;t,3cos t,3sin t&gt;dt               =∫0πtdt i+∫0π3cos tdt j+∫0π3sintdt k…

Q: Show that ¥(x,t)= Asin(wt+kx) describes a wave motion

A: Given: ψx,t=Asinwt+kx

Q: Show that F. dr is independent of its path, given that F(л, у, 2) — + tan 1+x² 2) i+ tanrj+ k. 1+2²…

A: We will show the required result.

Q: find the outward flux of F across the boundary of D.  F = 2xyi + 2yzj + 2xzk D: The cube cut from…

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Q: Sketch the direction field of the D.E. y = y - t and the solution curves corresponding to y(0) =-1,…

A: Solution of question is written in below steps.

Q: Suppose an object moves from (-1, 1) to (2, 4) along the path r(t) = (t, t²), subject to the force F…

A: Given that: F=xsiny, y and rt=t, t2 and object moves from (-1,1) to (2,4)

Q: Calculate the work done by the force F(x, y) = y?î+ xyj in moving a particle along the line which…

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Q: Evaluate the line integral [39a²³yzds with respect to s along the 2 curve C: x = t, y t, y = t²,₁…

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Q: Evaluate the line integral along the given paths.       C(x2 + y2) ds   a) C: line segment from (0,…

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Q: (a) Suppose that a black hole has magnetic field F = (2a* + e" sin(2), y³ + xe*, 2z³ + e" cos(z) +…

A: TO FIND: Magnetic flux across the black hole

Q: If F(x, y) = (6xy - 1,3x2 + 2y) and C is the circular arc along x² + y? = 2 from (1, 1) to (-1, 1),…

A: Given vector field is  F(x,y)=6xy-1,3x2+2yF(x,y)=(6xy-1)i+(3x2+2y)j c is the circular arc along…

Q: Evaluate the line integral C:y² = 30x from (30,30) to (0,0). NOTE: Enter the exact answer. [-ydr +…

A: line integral

Q: Consider the line integral xy dx + xy° dy with C the triangle with vertices (0, 0). (1,0), and (1,…

A: Given, the line integral Where C is the triangle with vertices.

Q: Suppose an object moves from (-1,2) to (1, 4) along the path r(t) = (t2,t ), |3D subject to the…

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Q: The work done by the force F = in the displacement along the path C: r(t)=from the point (1,0,0) to…

A: To find the work done by a force

Q: Set up an integral to compute the arc length L of the curve C: r(t) = (, 4t, v2t) %3D from the point…

A: I am going to setup an integral to compute the arc length of the given curve using the required…

Q: Find the work done in moving a point charge Q- - 20 1C from.the origin to (4,0,0) m in the ficld E-+…

A: To find - Find the work done in moving a point charge Q = -20 μC from the origin to 4, 0, 0m in the…

Q: Evaluate the line integral F. dr where F = (-3 sin x, cos y, 5xz) and C is the path given by r(t) =…

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Q: 4. Consider the closed curve C, which is the image of the path 7(t) = (a cos t, b sin t), t E [0,…

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Q: The velocity field for a flow is given by V = ut + vj + wk where u = 3x, y = -2y and w = 2z. Find…

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Q: Calculate the work done by F(x,y) = ⟨2x + ln( 2y2 −1), arctan(y4 +2y +1) + 4xy / (2y2 − 1⟩ along the…

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Q: A particle moves through 3-space in such a way that its acceleration is a(t) = 8 sin 2ti + 8 cos…

A: Gg

Q: Use Green's theorem to evaluate the line Integral for the curve C given in the figure. [2y dx + x…

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Q: find the flux of 3 – e")i+ (y³ + sin z)j+ (z³ – unded above by z = V4 – x² outward orientation.

A: We have to find the flux using the divergence therom according to the given information

Q: Calculate the line integral of F(x, y) = -4i + 5j along the line segment from (-3,-4) to (-5,0).…

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Q: Use Green's theorem to evaluate the line integral for the curve C given in the figure. [8y dx + 7x…

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Q: 3 2 Use a line integral to calculate the length of the helix ř(t) = (a cost, a sint, bt) 0<t < 2n…

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Q: (a) Identify the work done, S. F.dr by an electric field, Ē = (x + xy)î + (y + 5)ƒ – 5zk y2 V/m to…

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Q: he position x(t) of an object moving in 1-D on the a - aris in an inverse-square force held (such as…

A: As given by the question There are given that the equation of inverse-square force field is:…

Q: Let F = ( ) 5x* + 16z, 2x³ + 3y² + 16z, x + y + eVz³+1 and C be the curve defined by 7(t) = (2…

A: Given that,  F=5x4+16z, 2x3+3y2+16z, x+y+ez3+1 And rt=2cost, 2sint, 16cos2t sin2t, o≤t≤π To find…

Q: (2x + y)dx + (x + 2y)dy

A: Given integral is:  where C is any curve that joins the point (1,1) with the (2,2).

Q: Evaluate line integral F. dr, where F(x, y) =(2xy)i + (x²+3)j, and C is the path given by r(t) = t =…

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Q: Find the work done by the force F(r) = x2 +1 in moving a particle along the T-axis from r = 0 to r…

A: The work done by a variable force F(x) in moving a particle along the x-axis is given by the…