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- vector field F = ⟨b cos(ab) + 2a + b, a cos(ab) + 2b + a⟩. State if it is conservative with reasons.A particle starts at the point (-2,0), moves along the x-axis to (2,0) and then along the semicircle y=radical(4-x^2) to the starting point. Use Green’s Theorem to find the work done on this particle by the force field F(x,y) =(2x,x^3+3xy^2).Line segment D runs from (1, -4, 3) to (2, 0, -1). Determine how much work is done by the force field F(x, y, z) = <3y2/4, sin2(z+3), -cos2(2-y)>
- A particle starts at the point (-1, 0), moves along the x-axis to (1, 0), and then along the semicircle y = √(1 - x2 )to the starting point. Use Green's Theorem to find the work done on this particle by the force field F(x, y) = ‹3x, x3 + 3xy2›.Prove that divergence of vector potential 'A' is always zero.A particle starts at the point (−4, 0), moves along the x-axis to (4, 0), and then along the semicircle y = 16 − x2 to the starting point. Use Green's Theorem to find the work done on this particle by the force field F(x, y) = 5x, x3 + 3xy2 .