| 23. Find the outward flux of the field F = ( 3xy i + (e* + tan¯ly)j х 1 + y?, across the cardioid r = a(1 + cos 0), a > 0.

Q: Q6: Find the outward flux of the vector field F=(x²y+e'sin(y))i+ (x²+e'cos (y)) j through the right…

A: Given vector field is F=  x2y + ex siny  i + x2 + ex cosy j Curve r2=cos2θ

Q: 6. Let F = (x³ sin y, a* cos y). COS (a) Is F a conservative vector field? (b) If your answer to…

A:

Q: 1- Prove that the force field F known as : Prove that the force field defined by F = (y*z' -6xz? )i…

A:

Q: A vector field F = x(x² – y²) + ŷ(2xy + y?) a) f d.č =? c on the closed curve in the figure b)…

A: a) Consider the figure:

Q: Draw approx. solution for the directional field for the first order with the initial condition y(0)…

A: Given directional field:

Q: Show that the field F = (cos x)i + (- y sin y)j + (z3)k is conservative and Önd a potential function…

A: F = ( Cosx )i + ( -y Siny )j + ( z3 )k  F = gradient ( - Sinx - y Siny - Cosy + z4/4 ). Thus, we can…

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

A:

Q: Find the circulation of the Fİeld F(x; y) = 3xi+yj around the circle r(t) = (cos6t)i + ( sin6t)j;…

A: We need to find the circulation of field F→=3xi^+yj^  around the circle r→t=cos6ti^+sin6tj^ where…

Q: 6. Find the circulation of the field F(x, y) = -yi + x²j along the closed elliptical path x² + = 1…

A:

Q: Q6: Find the outward flux of the vector field F=(x²y+e'sin(y))i+ (x²+ e*cos(y))j through the right…

A: Solution

Q: 1. Find all the potential functions, if there are any, of the vector field F(x, y, z) = (2x sin(y −…

A: Given vector function is                  F→x,y,z…

Q: Find the curl of the vector field F (6x sin(y), 2y cos(x)). curl F =

A:

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

A:

Q: (i) An electrostatic field in xy-plane is given by $(x, y) = 3x²y- y³. Find the stream function Y…

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Q: Find the work done by the gradient vector field F(x, y, z) = V (e² + y² + z²) in %3| mov ing a…

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Q: 7. Find the outward flux of the field F(x, y) = -yi + x²j across the closed counter-clockwise curve…

A: Consider the given field: F→(x,y)=-yi^+x2j^ and