Final answer:
To determine the work done in carrying a +3μC charge from P₁(4,1,−1) to P₂ (16,2,−1) in the given electric field along the parabola x=4y², we can integrate the dot product of the force and displacement along the path.
Step-by-step explanation:
The work done in carrying a +3μC charge from P₁(4,1,−1) to P₂ (16,2,−1) in the field E =aₓy+aᵧx, along the parabola x=4y² can be found by integrating the dot product of the force and displacement along the path. The force is given by E = aₓy + aᵧx, and the displacement vector can be obtained by parameterizing the parabola equation. In this case, we can use x = 4y² as a parameterization, and substitute the values of x and y into the force equation to get the force vector at each point. Then, we can integrate the dot product of the force vector and the tangent vector along the path to find the work done.